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Borisov A. V., Kilin A. A., Pivovarova E. N.
In this paper we consider the control of the motion of a dynamically asymmetric unbalanced ball (Chaplygin top) by means of two perpendicular rotors. We propose a mechanism for control by periodically changing the gyrostatic momentum of the system, which leads to an unbounded speedup. We then formulate a general hypothesis of the mechanism for speeding up spherical bodies on a plane by periodically changing the system parameters.
Kilin A. A., Pivovarova E. N.
This paper presents a qualitative analysis of the dynamics in a fixed reference frame of a wheel with sharp edges that rolls on a horizontal plane without slipping at the point of contact and without spinning relative to the vertical. The wheel is a ball that is symmetrically truncated on both sides and has a displaced center of mass. The dynamics of such a system is described by the model of the ball’s motion where the wheel rolls with its spherical part in contact with the supporting plane and the model of the disk’s motion where the contact point lies on the sharp edge of the wheel. A classification is given of possible motions of the wheel depending on whether there are transitions from its spherical part to sharp edges. An analysis is made of the behavior of the point of contact of the wheel with the plane for different values of the system parameters, first integrals and initial conditions. Conditions for boundedness and unboundedness of the wheel’s motion are obtained. Conditions for the fall of the wheel on the plane of sections are presented.
Kilin A. A., Artemova E. M.
This paper is concerned with the problem of the interaction of vortex lattices, which is equivalent to the problem of the motion of point vortices on a torus. It is shown that the dynamics of a system of two vortices does not depend qualitatively on their strengths. Steadystate configurations are found and their stability is investigated. For two vortex lattices it is also shown that, in absolute space, vortices move along closed trajectories except for the case of a vortex pair. The problems of the motion of three and four vortex lattices with nonzero total strength are considered. For three vortices, a reduction to the level set of first integrals is performed. The nonintegrability of this problem is numerically shown. It is demonstrated that the equations of motion of four vortices on a torus admit an invariant manifold which corresponds to centrally symmetric vortex configurations. Equations of motion of four vortices on this invariant manifold and on a fixed level set of first integrals are obtained and their nonintegrability is numerically proved.
Ivanova T. B., Kilin A. A., Pivovarova E. N.
In this paper, we develop a model of a controlled spherical robot of combined type moving by displacing the center of mass and by changing the internal gyrostatic momentum, with a feedback that stabilizes given partial solutions for a free system at the final stage of motion. According to the proposed approach, feedback depends on phase variables (current position, velocities) and does not depend on the specific type of trajectory. We present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulations of motion with feedback that demonstrate the efficiency of the proposed model.
Borisov A. V., Kilin A. A., Karavaev Y. L., Klekovkin A. V.
The paper is concerned with the problem of stabilizing a spherical robot of combined type during its motion. The focus is on the application of feedback for stabilization of the robot which is an example of an underactuated system. The robot is set in motion by an inter- nal wheeled platform with a rotor placed inside the sphere. The results of experimental investigations for a prototype of the spherical robot are presented.
In this work we consider the controlled motion of a pendulum spherical robot on an inclined plane. The algorithm for determining the control actions for the motion along an arbitrary trajectory and examples of numerical simulation of the controlled motion are given.
This paper is concerned with a model of the controlled motion of a spherical robot with an axisymmetric pendulum actuator on an inclined plane. First integrals of motion and partial solutions are presented and their stability is analyzed. It is shown that the steady solutions exist only at an inclination angle less than some critical value and only for constant control action.
This paper is concerned with the dynamics of a wheel with sharp edges moving on a horizontal plane without slipping and rotation about the vertical (nonholonomic rubber model). The wheel is a body of revolution and has the form of a ball symmetrically truncated on both sides. This problem is described by a system of differential equations with a discontinuous right-hand side. It is shown that this system is integrable and reduces to quadratures. Partial solutions are found which correspond to fixed points of the reduced system. A bifurcation analysis and a classification of possible types of the wheel’s motion depending on the system parameters are presented.
In this paper, equations of motion for the problem of a ball rolling without slipping on a rotating hyperbolic paraboloid are obtained. Integrals of motions and an invariant measure are found. A detailed linear stability analysis of the ball’s rotations at the saddle point of the hyperbolic paraboloid is made. A three-dimensional Poincar´e map generated by the phase flow of the problem is numerically investigated and the existence of a region of bounded trajectories in a neighborhood of the saddle point of the paraboloid is demonstrated. It is shown that a similar problem of a ball rolling on a rotating paraboloid, considered within the framework of the rubber model, can be reduced to a Hamiltonian system which includes the Brower problem as a particular case.
Kilin A. A., Klenov A. I., Tenenev V. A.
This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal mechanisms, without changing the external shape of th e body. The paper presents an overview of theoretical papers that justify the possibility of this displacement in ideal and viscous liquids. A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the motion of two internal masses along the circles. The paper presents a mathematical model of the motion of a solid body with moving internal masses in a three-dime nsional formulation. This model takes into account the three-dimensional vibrations of the body during motion, which arise under the action of external forces-gravity force, Archimedes force and forces acting on the body, from the side of a viscous fluid. The body is a homogeneous elliptical cylinder with a k eel located along the larger diagonal. Inside the cylinder there are two material point masses moving along the circles. The centers of the circles lie on the smallest diagonal of the ellipse at an equal distance from the center of mass. Equations of motion of the system (a body with two mater ial points, placed in a fluid) are represented as Kirchhoff equations with the addition of external for ces and moments acting on the body. The phenomenological model of viscous friction is quadratic in velocity used to describe the forces of resistance to motion in a fluid. The coefficients of resistance to movement were determ ined experimentally. The forces acting on the keel were determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier – Stokes equations. In this paper, an experimental verification of the proposed mathematical model was carried out. Several series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained experimental data are compared with the results obtai ned within the framework of the proposed mathematical model.
In this paper, we develop a model of a controlled spherical robot with an axisymmetric pendulum-type actuator with a feedback system suppressing the pendulum’s oscillations at the final stage of motion. According to the proposed approach, the feedback depends on phase variables (the current position and velocities) and does not depend on the type of trajectory. We present integrals of motion and partial solutions, analyze their stability, and give examples of computer simulation of motion using feedback to illustrate compensation of the pendulum’s oscillations.
In the paper, a study of rolling of a dynamically asymmetrical unbalanced ball (Chaplygin top) on a horizontal plane under the action of periodic gyrostatic moment is carried out. The problem is considered in the framework of the model of a rubber body, i.e., under the assumption that there is no slipping and spinning at the point of contact. It is shown that, for certain values of the parameters of the system and certain dependence of the gyrostatic moment on time, an acceleration of the system, i.e., an unbounded growth of the energy of the system, is observed. Investigations of the dependence of the presence of acceleration on the parameters of the system and on the initial conditions are carried out. On the basis of the investigations of the dynamics of the frozen system, a conjecture concerning the general mechanism of acceleration at the expense to periodic impacts in nonholonomic systems is expressed.
In this paper, we show that the trajectories of a dynamical system with nonholonomic constraints can satisfy Hamilton’s principle. As the simplest illustration, we consider the problem of a homogeneous ball rolling without slipping on a plane. However, Hamilton’s principle is formulated either for a reduced system or for a system defined in an extended phase space. It is shown that the dynamics of a nonholonomic homogeneous ball can be embedded in a higher-dimensional Hamiltonian phase flow. We give two examples of such an embedding: embedding in the phase flow of a free system and embedding in the phase flow of the corresponding vakonomic system.
Borisov A. V., Kilin A. A., Karavaev Y. L.
This paper presents results of theoretical and experi- mental research explaining the retrograde final-stage rolling of a disk under certain relations between its mass and geometric parameters. Modifying the no-slip model of a rolling disk by including viscous rolling friction provides a qualitative explana- tion for the disk's retrograde motion. At the same time, the simple experiments described in the paper completely reject the aerodynamical drag torque as a key reason for the retro- grade motion of a disk considered, thus disproving some recent hypotheses.
Borisov A. V., Vetchanin E. V., Kilin A. A.
The motion of a body shaped as a triaxial ellipsoid and controlled by the rotation of three internal rotors is studied. It is proved that the motion is controllable with the exception of a few particular cases. Partial solutions whose combinations enable an unbounded motion in any arbitrary direction are constructed.
This paper is concerned with the dynamics of a top in the form of a truncated ball as it moves without slipping and spinning on a horizontal plane about a vertical. Such a system is described by differential equations with a discontinuous right-hand side. Equations describing the system dynamics are obtained and a reduction to quadratures is performed. A bifurcation analysis of the system is made and all possible types of the top’s motion depending on the system parameters and initial conditions are defined. The system dynamics in absolute space is examined. It is shown that, except for some special cases, the trajectories of motion are bounded.
Karavaev Y. L., Kilin A. A., Klekovkin A. V.
In this paper the model of rolling of spherical bodies on a plane without slipping is presented taking into account viscous rolling friction. Results of experiments aimed at investigating the influence of friction on the dynamics of rolling motion are presented. The proposed dynamical friction model for spherical bodies is verified and the limits of its applicability are estimated. A method for determining friction coefficients from experimental data is formulated.
Vetchanin E. V., Tenenev V. A., Kilin A. A.
In this paper we consider the controlled motion of a helical body with three blades in an ideal fluid, which is executed by rotating three internal rotors. We set the problem of selecting control actions, which ensure the motion of the body near the predetermined trajectory. To determine controls that guarantee motion near the given curve, we propose methods based on the application of hybrid genetic algorithms (genetic algorithms with real encoding and with additional learning of the leader of the population by a gradient method) and artificial neural networks. The correctness of the operation of the proposed numerical methods is estimated using previously obtained differential equations, which define the law of changing the control actions for the predetermined trajectory.
In the approach based on hybrid genetic algorithms, the initial problem of minimizing the integral functional reduces to minimizing the function of many variables. The given time interval is broken up into small elements, on each of which the control actions are approximated by Lagrangian polynomials of order 2 and 3. When appropriately adjusted, the hybrid genetic algorithms reproduce a solution close to exact. However, the cost of calculation of 1 second of the physical process is about 300 seconds of processor time.
To increase the speed of calculation of control actions, we propose an algorithm based on artificial neural networks. As the input signal the neural network takes the components of the required displacement vector. The node values of the Lagrangian polynomials which approximately describe the control actions return as output signals . The neural network is taught by the well-known back-propagation method. The learning sample is generated using the approach based on hybrid genetic algorithms. The calculation of 1 second of the physical process by means of the neural network requires about 0.004 seconds of processor time, that is, 6 orders faster than the hybrid genetic algorithm. The control calculated by means of the artificial neural network differs from exact control. However, in spite of this difference, it ensures that the predetermined trajectory is followed exactly.
Vetchanin E. V., Kilin A. A.
In this paper we study the controlled motion of an arbitrary two-dimensional body in an ideal fluid with a moving internal mass and an internal rotor in the presence of constant circulation around the body. We show that by changing the position of the internal mass and by rotating the rotor, the body can be made to move to a given point, and discuss the influence of nonzero circulation on the motion control. We have found that in the presence of circulation around the body the system cannot be completely stabilized at an arbitrary point of space, but fairly simple controls can be constructed to ensure that the body moves near the given point.
Kilin A. A., Bozek P., Karavaev Y. L., Klekovkin A. V., Shestakov V. A.
In this article, a dynamical model for controlling an omniwheel mobile robot is presented. The proposed model is used to construct an algorithm for calculating control actions for trajectories characterizing the high maneuverability of the mobile robot. A description is given for a prototype of the highly maneuverable robot with four omniwheels, for which an algorithm for setting the coefficients of the PID controller is considered. Experiments on the motion of the robot were conducted at different angles, and the orientation of the platform was preserved. The experimental results are analyzed and statistically assessed.
In this paper, we study the free and controlled motion of an arbitrary two-dimensional body with a moving internal material point through an ideal fluid in presence of constant circulation around the body. We perform bifurcation analysis of free motion (with fixed internal mass). We show that by changing the position of the internal mass the body can be made to move to a specified point. There are a number of control problems associated with the nonzero drift of the body in the case of fixed internal mass.
We consider the controlled motion in an ideal incompressible fluid of a rigid body with moving internal masses and an internal rotor in the presence of circulation of the fluid velocity around the body. The controllability of motion (according to the Rashevskii–Chow theorem) is proved for various combinations of control elements. In the case of zero circulation, we construct explicit controls (gaits) that ensure rotation and rectilinear (on average) motion. In the case of nonzero circulation, we examine the problem of stabilizing the body (compensating the drift) at the end point of the trajectory. We show that the drift can be compensated for if the body is inside a circular domain whose size is defined by the geometry of the body and the value of circulation.
Karavaev Y. L., Kilin A. A.
We present the results of theoretical and experimental investigations of the motion of a spherical robot on a plane. The motion is actuated by a platform with omniwheels placed inside the robot. The control of the spherical robot is based on a dynamic model in the nonholonomic statement expressed as equations of motion in quasivelocities with indeterminate coefficients. A number of experiments have been carried out that confirm the adequacy of the dynamic model proposed.
Vetchanin E. V., Kilin A. A., Mamaev I. S.
This paper is concerned with the motion of a helical body in an ideal fluid, which is controlled by rotating three internal rotors. It is proved that the motion of the body is always controllable by means of three rotors with noncoplanar axes of rotation. A condition whose satisfaction prevents controllability by means of two rotors is found. Control actions that allow the implementation of unbounded motion in an arbitrary direction are constructed. Conditions under which the motion of the body along an arbitrary smooth curve can be implemented by rotating the rotors are presented. For the optimal control problem, equations of sub-Riemannian geodesics on $SE(3)$ are obtained.
In this paper we describe the results of experimental investigations of the motion of a screwless underwater robot controlled by rotating internal rotors. We present the results of comparison of the trajectories obtained with the results of numerical simulation using the model of an ideal fluid.
Klenov A. I., Kilin A. A.
This paper is devoted to an experimental investigation of the motion of a rigid body set in motion by rotating two unbalanced internal masses. The results of experiments confirming the possibility of motion by this method are presented. The dependence of the parameters of motion on the rotational velocity of internal masses is analyzed. The velocity field of the fluid around the moving body is examined.
This paper is concerned with two systems from sub-Riemannian geometry. One of them is defined by a Carnot group with three generatrices and growth vector $(3, 6, 14)$, the other is defined by two generatrices and growth vector $(2, 3, 5, 8)$. Using a Poincaré map, the nonintegrability of the above systems in the general case is shown. In addition, particular cases are presented in which there exist additional first integrals.
This paper is concerned with the motion of an unbalanced heavy three-axial ellipsoid in an ideal fluid controlled by rotation of three internal rotors. It is proved that the motion of the body considered is controlled with respect to configuration variables except for some special cases. An explicit control that makes it possible to implement unbounded motion in an arbitrary direction has been calculated. Directions for which control actions are bounded functions of time have been determined.
In this paper, we develop the results obtained by J.Hadamard and G.Hamel concerning the possibility of substituting nonholonomic constraints into the Lagrangian of the system without changing the form of the equations of motion. We formulate the conditions for correctness of such a substitution for a particular case of nonholonomic systems in the simplest and universal form. These conditions are presented in terms of both generalized velocities and quasi-velocities. We also discuss the derivation and reduction of the equations of motion of an arbitrary wheeled vehicle. In particular, we prove the equivalence (up to additional quadratures) of problems of an arbitrary wheeled vehicle and an analogous vehicle whose wheels have been replaced with skates. As examples, we consider the problems of a one-wheeled vehicle and a wheeled vehicle with two rotating wheel pairs.
Bolsinov A. V., Kilin A. A., Kazakov A. O.
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: Pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane.
Klenov A. I., Vetchanin E. V., Kilin A. A.
This paper is concerned with the experimental determination of the added masses of bodies completely or partially immersed in a fluid. The paper presents an experimental setup, a technique of the experiment and an underlying mathematical model. The method of determining the added masses is based on the towing of the body with a given propelling force. It is known (from theory) that the concept of an added mass arises under the assumption concerning the potentiality of flow over the body. In this context, the authors have performed PIV visualization of flows generated by the towed body, and defined a part of the trajectory for which the flow can be considered as potential. For verification of the technique, a number of experiments have been performed to determine the added masses of a spheroid. The measurement results are in agreement with the known reference data. The added masses of a screwless freeboard robot have been defined using the developed technique.
Borisov A. V., Mamaev I. S., Kilin A. A., Bizyaev I. A.
This paper is concerned with the problem of the motion of a wheeled vehicle on a plane in the case where one of the wheel pairs is fixed. In addition, the motion of a wheeled vehicle on a plane in the case of two free wheel pairs is considered. A method for obtaining equations of motion for the vehicle with an arbitrary geometry is presented. Possible kinds of motion of the vehicle with a fixed wheel pair are determined.
Kilin A. A., Pivovarova E. N., Ivanova T. B.
This paper is concerned with free and controlled motions of a spherical robot of combined type moving by displacing the center of mass and by changing the internal gyrostatic momentum. Equations of motion for the nonholonomic model are obtained and their first integrals are found. Fixed points of the reduced system are found in the absence of control actions. It is shown that they correspond to the motion of the spherical robot in a straight line and in a circle. A control algorithm for the motion of the spherical robot along an arbitrary trajectory is presented. A set of elementary maneuvers (gaits) is obtained which allow one to transfer the spherical robot from any initial point to any end point.
A nonholonomic model of the dynamics of an omniwheel vehicle on a plane and a sphere is considered. A derivation of equations is presented and the dynamics of a free system are investigated. An explicit motion control algorithm for the omniwheel vehicle moving along an arbitrary trajectory is obtained.
This paper deals with the problem of a spherical robot propelled by an internal omniwheel platform and rolling without slipping on a plane. The problem of control of spherical robot motion along an arbitrary trajectory is solved within the framework of a kinematic model and a dynamic model. A number of particular cases of motion are identified, and their stability is investigated. An algorithm for constructing elementary maneuvers (gaits) providing the transition from one steady-state motion to another is presented for the dynamic model. A number of experiments have been carried out confirming the adequacy of the proposed kinematic model.
This paper presents the results of experimental investigations for the rolling of a spherical robot of combined type actuated by an internal wheeled vehicle with rotor on a horizontal plane. The control of spherical robot based on nonholonomic dynamical by means of gaits. We consider the motion of the spherical robot in case of constant control actions, as well as impulse control. A number of experiments have been carried out confirming the importance of rolling friction.
Kilin A. A., Vetchanin E. V.
In this paper we consider the problem of motion of a rigid body in an ideal fluid with two material points moving along circular trajectories. The controllability of this system on the zero level set of first integrals is shown. Elementary “gaits” are presented which allow the realization of the body’s motion from one point to another. The existence of obstacles to a controlled motion of the body along an arbitrary trajectory is pointed out.
The dynamic model for a spherical robot with an internal omniwheel platform is presented. Equations of motion and first integrals according to the non-holonomic model are given. We consider particular solutions and their stability. The algorithm of control of spherical robot for movement along a given trajectory are presented.
Kilin A. A., Karavaev Y. L., Klekovkin A. V.
In this article a kinematic model of the spherical robot is considered, which is set in motion by the internal platform with omni-wheels. It has been introduced a description of construction, algorithm of trajectory planning according to developed kinematic model, it has been realized experimental research for typical trajectories: moving along a straight line and moving along a circle.
Borisov A. V., Kilin A. A., Mamaev I. S., Tenenev V. A.
Fluid Dynamics Research, 2014, vol. 46, no. 3, 031415, 16 pp.
We consider the problem of motion of axisymmetric vortex rings in an ideal incompressible and viscous fluid. Using the numerical simulation of the Navier–Stokes equations, we confirm the existence of leapfrogging of three equal vortex rings and suggest the possibility of detecting it experimentally. We also confirm the existence of leapfrogging of two vortex rings with opposite-signed vorticities in a viscous fluid.
Borisov A. V., Kilin A. A., Mamaev I. S., Tenenev V. A., The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid , Fluid Dynamics Research, 2014, vol. 46, no. 3, 031415, 16 pp.
We investigate the motion of the point of contact (absolute dynamics) in the integrable problem of the Chaplygin ball rolling on a plane. Although the velocity of the point of contact is a given vector function of variables of the reduced system, it is impossible to apply standard methods of the theory of integrable Hamiltonian systems due to the absence of an appropriate conformally Hamiltonian representation for an unreduced system. For a complete analysis we apply the standard analytical approach, due to Bohl and Weyl, and develop topological methods of investigation. In this way we obtain conditions for boundedness and unboundedness of the trajectories of the contact point.
In our earlier paper  we examined the problem of control of a balanced dynamically nonsymmetric sphere with rotors with no-slip condition at the point of contact. In this paper we investigate the controllability of a ball in the presence of friction. We also study the problem of the existence and stability of singular dissipation-free periodic solutions for a free ball in the presence of friction forces. The issues of constructive realization of the proposed algorithms are discussed.
We consider the problem of motion of axisymmetric vortex rings in an ideal incompressible fluid. Using the topological approach, we present a method for complete qualitative analysis of the dynamics of a system of two vortex rings. In particular, we completely solve the problem of describing the conditions for the onset of leapfrogging motion of vortex rings. In addition, for the system of two vortex rings we find new families of motions where the relative distances remain finite (we call them pseudo-leapfrogging). We also find solutions for the problem of three vortex rings, which describe both the regular and chaotic leapfrogging motion of vortex rings.
We investigate the motion of the point of contact (absolute dynamics) in the integrable problem of the Chaplygin ball rolling on a plane. Although the velocity of the point of contact is a given vector function of variables of a reduced system, it is impossible to apply standard methods of the theory of integrable Hamiltonian systems due to the absence of an appropriate conformally Hamiltonian representation for an unreduced system. For a complete analysis we apply the standard analytical approach, due to Bohl and Weyl, and develop topological methods of investigation. In this way we obtain conditions for boundedness and unboundedness of the trajectories of the contact point.
In the paper we study the control of a balanced dynamically non-symmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic controllability is shown and the control inputs that steer the ball along a given trajectory on the plane are found. For some simple trajectories explicit tracking algorithms are proposed.
We discuss explicit integration and bifurcation analysis of two non-holonomic problems. One of them is the Chaplygin’s problem on no-slip rolling of a balanced dynamically non-symmetric ball on a horizontal plane. The other, first posed by Yu.N.Fedorov, deals with the motion of a rigid body in a spherical support. For Chaplygin’s problem we consider in detail the transformation that Chaplygin used to integrate the equations when the constant of areas is zero. We revisit Chaplygin’s approach to clarify the geometry of this very important transformation, because in the original paper the transformation looks a cumbersome collection of highly non-transparent analytic manipulations. Understanding its geometry seriously facilitate the extension of the transformation to the case of a rigid body in a spherical support – the problem where almost no progress has been made since Yu.N. Fedorov posed it in 1988. In this paper we show that extending the transformation to the case of a spherical support allows us to integrate the equations of motion explicitly in terms of quadratures, detect mostly remarkable critical trajectories and study their stability, and perform an exhaustive qualitative analysis of motion. Some of the results may find their application in various technical devices and robot design. We also show that adding a gyrostat with constant angular momentum to the spherical-support system does not affect its integrability.
In the paper we study control of a balanced dynamically nonsymmetric sphere with rotors. The no-slip condition at the point of contact is assumed. The algebraic contrability is shown and the control inputs providing motion of the ball along a given trajectory on the plane are found. For some simple trajectories explicit tracking algorithms are proposed.
We consider the problem of the motion of axisymmetric vortex rings in an ideal incompressible fluid. Using the topological approach, we present a method for complete qualitative analysis of the dynamics of a system of two vortex rings. In particular, we completely solve the problem of describing the conditions for the onset of leapfrogging motion of vortex rings. In addition, for the system of two vortex rings we find new families of motions in which the mutual distances remain finite (we call them pseudo-leapfrogging). We also find solutions for the problem of three vortex rings, which describe both the regular and chaotic leapfrogging motion of vortex rings.
In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.
We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. In contrast to the previously explored non-holonomic systems, this one has a higher dimension and is considerably more complicated. One remarkable property of our system is the existence of "clandestine" linear in momenta first integrals. For a more trivial integrable system, their counterparts were discovered by Chaplygin. We have also found a few cases of integrability.
The Hamiltonian representation and integrability of the nonholonomic Suslov problem and its generalization suggested by S. A. Chaplygin are considered. This subject is important for understanding the qualitative features of the dynamics of this system, being in particular related to a nontrivial asymptotic behavior (i. e., to a certain scattering problem). A general approach based on studying a hierarchy in the dynamical behavior of nonholonomic systems is developed.
We consider a nonholonomic model of the dynamics of an omni-wheel vehicle on a plane and a sphere. An elementary derivation of equations is presented, the dynamics of a free system is investigated, a relation to control problems is shown.
We consider the problem of explicit integration and bifurcation analysis for two systems of nonholonomic mechanics. The first one is the Chaplygin’s problem on no-slip rolling of a balanced dynamically non-symmetrical ball on a horizontal plane. The second problem is on the motion of rigid body in a spherical support. We explicitly integrate this problem by generalizing the transformation which Chaplygin applied to the integration of the problem of the rolling ball at a non-zero constant of areas. We consider the geometric interpretation of this transformation from the viewpoint of a trajectory isomorphism between two systems at different levels of the energy integral. Generalization of this transformation for the case of dynamics in a spherical support allows us to integrate the equations of motion explicitly in quadratures and, in addition, to indicate periodic solutions and analyze their stability. We also show that adding a gyrostat does not lead to the loss of integrability.
We consider a novel mechanical system consisting of two spherical bodies rolling over each other, which is a natural extension of the famous Chaplygin problem of rolling motion of a ball on a plane. In contrast to the previously explored non-holonomic systems, this one has a higher dimension and is considerably more complicated. One remarkable property of our system is the existence of «clandestine» linear in momenta first integrals. For a more trivial integrable system, their counterparts were discovered by Chaplygin. We have also found a few cases of integrability.
Borisov A. V., Bolotin S. V., Kilin A. A., Mamaev I. S., Treschev D. V.
We consider the problems of Hamiltonian representation and integrability of the nonholonomic Suslov system and its generalization suggested by S. A. Chaplygin. These aspects are very important for understanding the dynamics and qualitative analysis of the system. In particular, they are related to the nontrivial asymptotic behaviour (i. e. to some scattering problem). The paper presents a general approach based on the study of the hierarchy of dynamical behaviour of nonholonomic systems.
We consider the motion of a material point on the surface of a sphere in the field of $2n + 1$ identical Hooke centers (singularities with elastic potential) lying on a great circle. Our main result is that this system is superintegrable. The property of superintegrability for this system has been conjectured by us in , where the structure of a superintegral of arbitrarily high odd degree in momemnta was outlined. We also indicate an isomorphism between this system and the one-dimensional $N$-particle system discussed in the recent paper  and show that for the latter system an analogous superintegral can be constructed.
Borisov A. V., Mamaev I. S., Kilin A. A.
The dynamics of self-gravitating liquid and gas ellipsoids is considered. A literary survey and authors’ original results obtained using modern techniques of nonlinear dynamics are presented. Strict Lagrangian and Hamiltonian formulations of the equations of motion are given; in particular, a Hamiltonian formalism based on Lie algebras is described. Problems related to nonintegrability and chaos are formulated and analyzed. All the known integrability cases are classified, and the most natural hypotheses on the nonintegrability of the equations of motion in the general case are presented. The results of numerical simulations are described. They, on the one hand, demonstrate a chaotic behavior of the system and, on the other hand, can in many cases serve as a numerical proof of the nonintegrability (the method of transversally intersecting separatrices).
Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector. A corresponding algebra of integrals constituted by the integrals of momentum, angular momentum, and Galilean momentum is presented. Particle systems with a particleinteraction potential homogeneous of degree $\alpha = –2$ are considered. The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. A new nonlinear algebra of integrals including the Jacobi integral is found. A systematic description is given to a new reduction procedure and possibilities of applying it to dynamics with the aim of lowering the order of Hamiltonian systems.
Some new integrable and superintegrable systems generalizing the classical ones are also described. Certain generalizations of the Lagrangian identity for systems with a particle interaction potential homogeneous of degree $\alpha = –2$ are presented. In addition, computational experiments are used to prove the nonintegrability of the Jacobi problem on a plane.
3-particle systems with a particle-interaction homogeneous potential of degree $α=-2$ is considered. A constructive procedure of reduction of the system by 2 degrees of freedom is performed. The nonintegrability of the systems is shown using the Poincare mapping.
Systems of material points interacting both with one another and with an external field are considered in Euclidean space. For the case of arbitrary binary interaction depending solely on the mutual distance between the bodies, new integrals are found, which form a Galilean momentum vector.
A corresponding algebra of integrals constituted by the integrals of momentum, angular momentum, and Galilean momentum is presented. Particle systems with a particle-interaction potential homogeneous of degree $α=-2$ are considered. The most general form of the additional integral of motion, which we term the Jacobi integral, is presented for such systems. A new nonlinear algebra of integrals including the Jacobi integral is found. A systematic description is given to a new reduction procedure and possibilities of applying it to dynamics with the aim of lowering the order of Hamiltonian systems.
Some new integrable and superintegrable systems generalizing the classical ones are also described. Certain generalizations of the Lagrangian identity for systems with a particle-interaction potential homogeneous of degree $α=-2$ are presented. In addition, computational experiments are used to prove the nonintegrability of the Jacobi problem on a plane.
We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball at the upmost, downmost and saddle point.
In this paper, we consider the transition to chaos in the phase portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotization are indicated: (1) the growth of the homoclinic structure and (2) the development of cascades of period doubling bifurcations. On the zero level of the area integral, an adiabatic behavior of the system (as the energy tends to zero) is noted. Meander tori induced by the break of the torsion property of the mapping are found.
For the classical problem of motion of a rigid body about a fixed point with zero area integral, we present a family of solutions that are periodic in the absolute space. Such solutions are known as choreographies. The family includes the well-known Delone solutions (for the Kovalevskaya case), some particular solutions for the Goryachev–Chaplygin case, and the Steklov solution. The "genealogy" of solutions of the family naturally appearing from the energy continuation and their connection with the Staude rotations are considered. It is shown that if the integral of areas is zero, the solutions are periodic with respect to a coordinate frame that rotates uniformly about the vertical (relative choreographies).
The paper contains the review and original results on the dynamics of liquid and gas self-gravitating ellipsoids. Equations of motion are given in Lagrangian and Hamiltonian form, in particular, the Hamiltonian formalism on Lie algebras is presented. Problems of nonintegrability and chaotical behavior of the system are formulated and studied. We also classify all known integrable cases and give some hypotheses about nonintegrability in the general case. Results of numerical modelling are presented, which can be considered as a computer proof of nonintegrability.
We discuss system of material points in Euclidean space interacting both with each other and with external field. In particular we consider systems of particles whose interacting is described by homogeneous potential of degree of homogeneity $\alpha=-2$. Such systems were first considered by Newton and—more systematically—by Jacobi). For such systems there is an extra hidden symmetry, and corresponding first integral of motion which we call Jacobi integral. This integral was given in different papers starting with Jacobi, but we present in general. Furthermore, we construct a new algebra of integrals including Jacobi integral. A series of generalizations of Lagrange's identity for systems with homogeneous potential of degree of homogeneity $\alpha=-2$ is given. New integrals of motion for these generalizations are found.
The dynamics of an antipodal vortex on a sphere (a point vortex plus its antipode with opposite circulation) is considered. It is shown that the system of n antipodal vortices can be reduced by four dimensions (two degrees of freedom). The cases $n = 2, 3$ are explored in greater detail both analytically and numerically. We discuss Thomson, collinear and isosceles configurations of antipodal vortices and study their bifurcations.
The paper considers the dynamics of a rattleback as a model of a heavy balanced ellipsoid of revolution rolling without slippage on a fixed horizontal plane. Central ellipsoid of inertia is an ellipsoid of revolution as well. In presence of the angular displacement between two ellipsoids, there occur dynamical effects somewhat similar to the reverse fenomena in earlier models. However, unlike a customary rattleback model (a truncated biaxial paraboloid) our system allows the motions which are superposition of the reverse motion (reverse of the direction of spinning) and the turn over (change of the axis of rotation). With appropriate values of energies and mass distribution, this effect (reverse + turn over) can occur more than once. Such motions as repeated reverse or repeated turn over are also possible.
The paper considers the process of transition to chaos in the problem of four point vortices on a plane. A new method for constructive reduction of the order for a system of vortices on a plane is presented. Existence of the cascade of period doubling bifurcations in the given problem is indicated.
Rolling (without slipping) of a homogeneous ball on an oblique cylinder in different potential fields and the integrability of the equations of motion are considered. We examine also if the equations can be reduced to a Hamiltonian form. We prove the theorem stated that if there is a gravity (and the cylinder is oblique), the ball moves without any vertical shift, on the average.
We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball in the upmost, downmost and saddle point.
In this paper we describe new classes of periodic solutions for point vortices on a plane and a sphere. They correspond to similar solutions (so-called choreographies) in celestial mechanics.
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a system with two degrees of freedom and give a number of remarkable periodic orbits. We also discuss integrability and stochastization of the motion.
We obtained new periodic solutions in the problems of three and four point vortices moving on a plane. In the case of three vortices, the system is reduced to a Hamiltonian system with one degree of freedom, and it is integrable. In the case of four vortices, the order is reduced to two degrees of freedom, and the system is not integrable. We present relative and absolute choreographies of three and four vortices of the same intensity which are periodic motions of vortices in some rotating and fixed frame of reference, where all the vortices move along the same closed curve. Similar choreographies have been recently obtained by C. Moore, A. Chenciner, and C. Simo for the $n$-body problem in celestial mechanics [6, 7, 17]. Nevertheless, the choreographies that appear in vortex dynamics have a number of distinct features.
In the paper we present the qualitative analysis of rolling motion without slipping of a homogeneous round disk on a horisontal plane. The problem was studied by S.A. Chaplygin, P. Appel and D. Korteweg who showed its integrability. The behavior of the point of contact on a plane is investigated and conditions under which its trajectory is finit are obtained. The bifurcation diagrams are constructed.
The problem of rolling motion without slipping of an unbalanced ball on 1) an arbitrary ellipsoid and 2) an ellipsoid of revolution is considered. In his famous treatise E. Routh showed that the problem of rolling motion of a body on a surface of revolution even in the presence of axisymmetrical potential fields is integrable. In case 1, we present a new integral of motion. New solutions expressed in elementary functions are found in case 2.
The paper is concerned with the problem on rolling of a homogeneous ball on an arbitrary surface. New cases when the problem is solved by quadratures are presented. The paper also indicates a special case when an additional integral and invariant measure exist. Using this case, we obtain a nonholonomic generalization of the Jacobi problem for the inertial motion of a point on an ellipsoid. For a ball rolling, it is also shown that on an arbitrary cylinder in the gravity field the ball's motion is bounded and, on the average, it does not move downwards. All the results of the paper considerably expand the results obtained by E. Routh in XIX century.
The motion of Chaplygin ball with and without gyroscope in the absolute space is analyzed. In particular, the trajectories of the point of contact are studied in detail. We discuss the motions in the absolute space, that correspond to the different types of motion in the moving frame of reference related to the body. The existence of the bounded trajectories of the ball's motion is shown by means of numerical methods in the case when the problem is reduced to a certain Hamiltonian system.
In the paper Motion of a circular cylinder and a vortex in an ideal fluid (Reg. & Chaot. Dyn. V. 6. 2001. No 1. P. 33-38) Ramodanov S.M. showed the integrability of the problem of motion of a circular cylinder and a point vortex in unbounded ideal fluid. In the present paper we find additional first integral and invariant measure of motion equations.
Borisov A. V., Kilin A. A.
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems are also formulated.
We consider two-body problem and restricted three-body problem in spaces $S^2$ and $L^2$. For two-body problem we have showed the absence of exponential instability of partiбular solutions relevant to roundabout motion on the plane. New libration points are found, and the dependence of their positions on parameters of a system is explored. The regions of existence of libration points in space of parameters were constructed. Basing on a examination of the Hill's regions we found the qualitative estimation of stability of libration points was produced.


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industry_corpus2: Real Estate & Construction


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A storm is brewing at Gaborone United as they reel from financial woes. With players reportedly boycotting training requesting to be paid, the club has also lost its chairman Rapula Okaile who resigned on Wednesday. Okaile’s unexpected resignation comes at a time when the club is struggling financially that even players have not been paid for some time. This week one of the players confirmed their boycott, saying they are demanding their dues before they could get back into the pitch. The player, who spoke on condition of anonymity for fear of victimisation, said the players feel that management is not serious to address their issue. He said they are constantly tricked with promises of being paid the next day, but that never happens. Gaborone United have been going through a rough financial patch since the departure of its former Director and Financier Nikolas Zakhem. It is believed that Okaile’s departure from the club will further worsen the situation. GU General Manager Olebile Sikwane confirmed that indeed Okaile has tendered his resignation. Sikwane said in the letter Okaile cited personal problems as the reason for his resignation. He said GU thank him for the selfless contribution he made to the club. Under his leadership this season GU experienced an improved performance both in the league and the Mascom Top 8. Contacted for comment Okaile confirmed his resignation, explaining that it is due to personal reasons. He, however, could not divulge more on the reasons. Okaile has since relinquished the Botswana Premier League Board chairmanship as well. While personal reasons are cited for his departure those close to GU believe that Okaile might have been forced out. Since assuming the chairmanship Okaile has known no peace. He was, however, adamant and held on for the past two years though a faction challenged the legality of his election to the position.The matter even reached the court of laws.
With the club having failed to hold its Annual General Meetings (AGMs) in three consecutive years because of failing to form quorum some believe that this was sabotage to stall progress. The battle for club control led to Zakhem’s exit from GU which ignited the financial problems that are now haunting the team. With Okaile leaving the team, it remains to be seen if the head coach Rudolf Zapata will last in his position. Those who know say Zapata is still holding the position because Okaile was protecting him. To try and alleviate the financial problem at the club, reports are rife that former financier has offered to help pay players wages for a month. Though the sources say he will just be helping out some revealed that Zakhem is harbouring desires to return to GU. Contacted for comment Zakhem confirmed that he had offered to help GU pay the players a month and half salary arrears. “Yes, I have spoken to the players on Friday after meeting with Mr Rapula Okaile, and relayed on his behalf to the players that they will be paid a month and half of their salaries arrears. Mr Okaile requested for financial assistance to top up Mascom prize money to cover 1.5 month players’ salary,” confirmed Zakhem. However, the former GU director quashed reports that he wants to return to GU. With Okaile out it remains to be seen who will be taking over as Gaborone United’s chairman. Sikwane, however, called on the Gaborone United supporters to remain calm throughout the transition period.

industry_corpus2: Sports


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Blueprint Pro Wrestling returns SOON!
Come and see the rising stars!
Don't miss the action and intensity that makes up BLUEPRINT Pro Wrestling in Deerfield Beach, Florida!!!
BLUEPRINT PRO WRESTLING is an independent wrestling organization based out of the South Florida area.
BLUEPRINT PRO WRESTLING will have more information on the next event date in the upcoming days. Stay tuned!
At Blueprint Pro Wrestling: Dimensions, the New Age Outlaw himself, BILLY GUNN, entered himself into the main event picture against The Storm and Austin Theory, in a triple threat match! What action is in store when Blueprint Pro returns SOON? ANYTHING can happen!
Welcome to BLUEPRINT Pro Wrestling! Our events are located in Deerfield Beach, FLA at the DS Sports Plex, at 3650 SW 10th St, Deerfield Beach, FL 33442.
Catch all of the ACTION and INTENSITY as our gladiators bring everything they have to the BLUEPRINT ring for an opportunity to showcase their talents on their way to victory!
Copyright © 2017 BLUEPRINT Pro Wrestling - All Rights Reserved.


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Today I am feeling inspired by the people around me.
More specifically, I am inspired by those who live with the intention to connect with those around them, those who create a sense of belonging both for themselves and others, those who value the concept of community. By our very nature we are social creatures, and I feel that as a society (specifically the millennial generation) our social lives are both on over-drive, but at the same time a little lost.
Recently, through my work, I supported a webinar that featured a neighbourhood project out west called Abundant Community Edmonton. While on this webinar, Anne Harvey from the City of Edmonton said something that struck me – she said that "as communities we have lost the art of neighbourliness." I began to think about this and Anne couldn’t be more right. Although there are many people, associations and groups that volunteer their time create a sense of community where they live, the reality is that the majority of us have truly lost the art of neighbourliness. In a world where we are capable of being connected to one another on a constant basis – we seem to be so disconnected.
I strongly believe that community doesn’t have to be where you reside, although for many people it is – community is about where we spend our time and where we create connections and build relationships. So the question that arises is this: How do we bring the art of neighbourliness online?
I am also a strong believer in the positive potential of technology and social media, however, I think it’s time we take a step back and reflect on how we exist in our corners of the universe. Now is as good a time as any to make our online worlds just a little more meaningful.
To you, my fellow millennials, I extend a challenge!
Out in public and you see that person you’ve been creeping? Smile and say hello! Let them know you recognize them from the dance videos they post, the hilarious selfies they take or the inspirational words they share – let’s be real we don’t post just to post, we post to share with others, let’s stop pretending it’s weird to acknowledge that!
Notice someone’s posts have been a little blue? Reach out to them.
Find something online you think someone else really needs to see – tag them in it!
And last but not least, never forget the value of attentive face-to-face connection and real human experience – implement the cellphone pile once in a while!
This post was an excerpt from the "We Ponder" blog where it was originally published. Read the full post here, and check out other musings on"We Ponder"
Sienna Jae Taylor has a love for all things community and a deep passion for positive, social change. She recently worked with the Tamarack Institute as a Community Animator and previous to that was a member of the Pillar Nonprofit Network team as the 2015 ChangeTheWorld Coordinator. Sienna brings to her work experience in community engagement and animation, strength and creativity in the art of communication and a natural flair for relationship building. Sienna is motivated by the incredible world-changers and inspiring projects that she encounters everyday and believes that with a little community, celebration and passion, anything is possible.

industry_corpus2: Subject Education


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A book in a box.
A new idea. I constantly have new ideas about how to write books, and then I write those books the same way, or whatever way is most convenient. Because, you know, writing the book is the most important thing.
The world is full of people who have important books they never write.
My current book started off strong and wrong. No recovering from that. I love it. It's probably my stupidest book and yet my favorite, but because of that I can look at it and see how it might have been even better.
So the basic problem is: I discover a story in the the writing of the story. Simple as that.
I've never, ever written a book I've diagrammed in advance. I always found too much wrong with the story and never wrote it.
Maybe I'm saying, ignorance is bliss. Not knowing that the story won't quite work out is enough to keep me writing until I discover different.
I try to come up with a concept, a premise for a book that I think is strong and needs some thought and development and research.
So I grab a box--a nice Diamond shipping box--and I put the tentative title on the box in black ink and then every time I have a thought, I write it down and throw it into the box. And then...someday...I'll know when I have enough material to proceed.
Silly idea, but I might try it.
Newer PostThe SF and Fantasy Canon, according to...well, me.

industry_corpus2: Literature & Emotions


text:
US state of Texas pumped more than three million barrels per day in April, almost equivalent to Iraq's monthly production.
The government's wage bill and ongoing economic uncertainty present risks to financial sustainability, warns the Treasury.
Jaitley, who also holding the Defence and Corporate Affairs portfolio, conveyed the message to Tuki when he met him in New Delhi yesterday, the release said.
Frances O'Grady, general secretary of the TUC, says no recovery for public sector staff.
Britain slams France, Spain and Italy for not doing enough' in international relief effort.
Juma on Piketty's Capital: can Africa avoid the trap of unequal growth?
With the recent price moves, the metal has shaped a flag pattern and is now testing resistance at $1334.50.
Commerce Secretary Rajeev Kher, who is in Tokyo, said that "India is rebranding itself as not only the pharmacy to the world, but also the responsible health care giver to the world."
Moody's expects the new government to increase the retail selling prices of controlled fuel products - kerosene and liquefied petroleum gas (LPG) -- to help control its subsidy burden.
The cotton consumption by mills in non-SSI and SSI sectors stood at 286.46 lakh bales, registering an increase of 8.86 percent over previous year's 263.15 lakh bales.
The increase in consumer confidence points to some resilience in the consumer sector in the face of considerable headwinds, according to an index.
India raises minimum export price for onions to maintain domestic price levels as fears grow of a shortage because of adverse weather conditions.
As Puerto Rico’s electric company struggles to pay its debts, the governor signed a law allowing public corporations to seek protection similar to what bankruptcy provides.
Eurozone's investment gap is 2% of gross domestic product or around €200bn annually, according to German Institute for Economic Research.
The UK construction industry grew at its fastest pace in four months in June, a survey suggests, with companies hiring staff at a record rate.
Sheryl Sandberg, COO, Facebook, emphasized on Indiaâs importance to global economy. Speaking at a Ficci event -- The Power to Empower â she discusses on various issues faced by todayâs women â from healthcare to gender bias.
Markit PMI for UK construction shows sector building on powerful recovery and adding jobs.
A wage agreement has been reached between employers in the carpet sector and the SA Clothing and Textile Workers' Union.
The Steel and Engineering Industries Federation of SA is concerned about South Africa's shrinking economy caused by strike action.
Eskom workers affiliated to Numsa plan to picket outside the company's headquarters in Megawatt Park, Johannesburg, in support of their 12% wage hike demand.
Brent crude futures stubborn above $112 a barrel as Iraq government struggles to defeat insurgency.
Numsa general secretary Irvin Jim says wage talks with an employers' group will resume later in the week.
World Bank data shows that the principality leads Liechtenstein and Bermuda.
UK house prices rose above their peak of 2007, rising 1% in June and 11.8% higher than a year earlier, the Nationwide says.
The Reserve Bank has launched a new R5 coin to celebrate 20 years of democracy and answers a Fin24 user's query why pre-2004 R5 coins are still in circulation.
Last month, the minimum export price (MEP) on onion was re-introduced at USD 300 per tonne barely three months after the previous government in March had abolished it. MEP is the rate below which no exports are allowed.
Youth joblessness remains remarkably high across the country, threatening long-term trouble for young people's career trajectories, earning potential and the overall health of the economy.
Move is part of BoE governor Mark Carney's efforts to restructure the central bank's operations.
Exports will now be possible only at or above $500 per tonne. The government on June 17 set the minimum price at $300 per tonne.
Empty lots have multiplied in parts of Chicago in recent years, so the city is selling them to homeowners dirt cheap. It's an effort to spark renewal in some of the city's most blighted areas.
In an interview to CNBC-TV18âs Anuj Singhal and Ekta Batra, S Ramnath, CFO, ITD Cementation spoke about the companyâs fund raising plans and the road ahead.
Companies say it pays to invest in employee health — productivity climbs and many costs of health care drop. But preserving worker privacy while encouraging fitness can be tricky.
Twenty years ago, first July 1994, after decades of financial turmoil, Brazil introduced its current currency, the Real, marking a turning point in the country's fight against hyperinflation.
The Falkland Islands Government have minted a new circulatory £2 coin, to mark the Centenary of the Battle of the Falkland Islands in 1914.
British house prices have risen at the fastest annual pace in more than nine years and prices in London have shown their biggest jump in a generation.
The near 4% rally of USD/INR since 22 May failed below 60.91, a main Fibonacci level. Also, a bearish signal has been triggered for the pair by the MACD on the daily chart.

industry_corpus2: Petrochemicals


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* How long does Marmaris Buggy Safari excursion take from Marmaris ?
* What is included in the price of the Marmaris Buggy Safari excursion from Marmaris ?
* What is not included in the price of the Marmaris Buggy Safari excursion from Marmaris ?
* Which language guide will be speaking to us on Marmaris Buggy Safari excursion from Marmaris ?
* Are there any restrictions on Marmaris Buggy Safari excursion in Marmaris ?
* What should I bring to Marmaris Buggy Safari excursion from Marmaris ?
* Do I need my Marmaris Buggy Safari excursion voucher to be printed ?
* When and where can I join Marmaris Buggy Safari excursion from Marmaris ?
* How do I get picked up for Marmaris Buggy Safari excursion in Marmaris ?
* What are the Highlights of Marmaris Buggy Safari excursion from Marmaris ?

industry_corpus2: Travel & Geography


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At networking meetings I tend to meet the people I am meant to meet. Magically we seem to gravitate towards like minded people. So conversations flow easily. Most of the time we aren’t even talking about business. We are getting to know each other better and choose to meet up again afterwards as we’ve run out of time and there’s more to discuss.
And now I see there is another thread throughout my life, I am a confidante. People tell me their inner most thoughts which means I am a trusted keeper of stories and secrets. I don’t ask them to share. It just happens. And these days more frequently.
Random conversations are powerful. Especially the heartfelt ones.
But the conversation isn’t always about others needing to offload. Sometimes someone I meet will share a nugget of wisdom that is precisely what I need to hear in the moment. They gift me an insight. A piece of wisdom. Share necessary guidance. Reaffirm something. They tell me something important that I need to hear so I know I am on the right track.
For some time I had been deliberating whether or not to create my own group for women. My idea had bubbled away for several years. It was about connection. Deeper conversation. Honesty. Encouragement. Collective growth. For women.
There are some people who could hear you speak a thousand words and still not understand you.
I held the vision of me standing in an unknown place, and one by one women would step forward and stand alongside me. We’d be collectively together.
This vision became a frequent visitor.
And yet, there were plenty of reasons why I didn’t pursue it further at the time. The concept wasn’t quite there. I struggled to find the right venue. I couldn’t fully articulate my ideas. I didn’t want to write a typical sales page. I had too much going on at home. And who would be interested anyway?
But still, I continued to wonder if other women out there were seeing and feeling what I was?
Did they see that even in this day and age women were still being overlooked?
Could they sense that something was beginning to shift?
That women were finding their their voices and were courageously beginning to speak out about the things that truly mattered?
Did they feel as strongly as I do about the women out there who have powerful gifts and valuable insights to share who are being ridiculed, ignored and suppressed?
I wasn’t so sure. So my frustration and the idea remained just that, an idea.
Last year an unexpected but significant conversation occurred in my local supermarket.
Unbeknownst to me I was about to meet someone very special in my local supermarket and have a conversation that would change how I went about my work and business.
Whilst standing in the queue an elderly man on a mobility scooter was in front of me. He paid for his shopping and made off to leave but accidentally hit the power on his scooter too hard. He ended up crashing into a bench located on the other side of the aisle.
We all laughed. (He was OK I really don’t just go around laughing at the misdemeanors of elderly men on their scooters!).
And the lovely check out lady said “You can have my L plates, as I have just passed my driving test”.
We laughed some more and fortunately he made it out of the shop unscathed.
I began to pack my shopping and said to her how brilliant it was that she’d passed her driving test and freedom beckoned.
Suddenly the conversation took a more serious tone.
She looked up at me and said “If only”.
With tears in her eyes she shared that she had spent the last eight years trying to learn how to drive. Now that she had passed her husband wouldn’t allow her to use the car. He didn’t want her to drive herself anywhere without him. He had to know exactly what she was doing and with whom at all times.
She went on to explain that in her culture you do not disobey your husband.
And yet here she was in a country surrounded by women with opportunities and their freedom. Why couldn’t she have the same?
In that moment I saw her. Really saw her. I could immediately sense what she was not saying aloud.
Something profound passed between us.
She continued to say that since moving to the UK she was more unhappy than she’d ever been. Because her freedom had been taken away. Before she moved here and married her husband she was free. And now she wasn’t.
This was not the life her mother had intended for her and she had decided it was too late to change. But she would do everything in her power to ensure her young daughter’s life would be very different than her own.
I nodded. I heard her. I understood. I felt her pain and anguish. And I wished her life was different too.
She asked me what I do. So I told her that I am fortunate to have my freedom. That I am able to work with brilliant women who have theirs too. Some have their own businesses. Many are on a powerful mission. Or they may use their voice to share their stories. Or they may even want to do something more meaningful but are not sure how. So I help them. To be the change that many of us desperately wish to see in our lifetime.
And what she said next has stayed with me ever since.
She told me that I must do everything I can to help the women around me. To embrace my freedom. To speak up on her behalf. To do what I can for those who for whatever reason cannot.
And I also told her that it is never too late for her to change her life for the better. She deserved to be happy. And she was just as entitled to her freedom, like me.
I left the shop and drove home with a heavy heart and tears. Because how could this still be happening to women in our lifetime?
But the sad truth is it is. And a lot more.
So I knew it was time for me to follow her advice. She had given me a powerful insight. I’d met her for a reason. And every time I go into the supermarket I look for her. But I have never seen her since.
If ever I needed a sign or a nudge or a monumental kick up the arse from the Universe. The powers that be. Whatever you choose to call it. THIS was it.
Instinctively I knew what I had to do. I had to get out of my own way and trust and believe that what I saw and felt, others did too. It was time for this idea of mine to become a reality.
So I created and launched the Social Collective.
The Social Collective came together following this heartfelt conversation with a brave woman who trusted me enough to tell me her story.
I am eternally grateful to her. And if I see her again, which I hope I do, I will tell her that because of her all of us within the Collective have since gone on to transform ourselves, our lives and our businesses. Who knows this domino effect may have transformed those around us and our tribes too?
I consciously created the Social Collective for women. Soulful women. Women on a mission. Women who know they are capable of more. Women who have their freedom of speech. Women who know they have something important to share. Women who want to serve. Women who want to empower others. Women who have something important to do. Women who are brave, courageous and sometimes afraid. Women who are willing to be vulnerable and share their stories in order to help others in their time of need. Women who are willing to readdress the balance between the masculine and feminine. Women who say we’ve had enough of being ignored, overlooked, suppressed and belittled. Women who are simply the change.
And I promised her I would. For her and her daughter. For me and for my beloved Grace. For my beautiful nieces. For all the women who are willing to be the change. And even more so for those around us who cannot be.
Because things HAVE to change. Don’t they?
The Dalai Lama said that the world will be saved by the Western Woman.
I now realise this is not because we are the only ones with insightful wisdom or magical feminine powers. It’s because we may have more freedom than others.
We have the tools ready and waiting at our disposal. We can express our voices to speak our truth. We are stepping forward and rising so others can see and hear us.
But we have to choose. Are we in or out?
There are many reasons why I choose to work with soulful women. I will share more of my why’s another time.
But it is my intention to do whatever it takes to change the world for the women I meet and work with. I can show others how to leverage the internet and social media to raise awareness of a meaningful campaign. I can demonstrate and teach how to create and market a petite business that comes from the heart. I will continue to use my voice to tell stories that speak the truth. And I know and wholeheartedly believe that the time is now for us wonderful women to lead with our wisdom.
So this is just some of the work we do within the Social Collective.
A circle of women may just be the most powerful force known to humanity. If you have one embrace it. If you need one, seek it. If you find one for the love of all that is good and holy, dive in. Hold on. Love it up.
Get naked. Let them see you. Let them hold you. Let your reluctant tears fall. Let yourself rise and love gentle. You will be changed. The very fabric of your being will be altered by this. If you allow it.
With all of my work we focus on you. The real woman within. We get re-acquainted and reconnect with her to understand what she is really here to do. And why.
So that’s you in your entirety. Not just your business. Not just you personally. Everything. Because you are the driving force. Without YOU nothing happens. Nothing changes.
And change and transformation is long overdue.
Saudi Arabia was the only country left in the world where women were not allowed to drive. That began to change in June 2018.
I relish my freedom and I was fortunate that my Dad taught me how to drive as soon as I could at 17. And he taught my Mum. And my sister. Because he wanted us to be independent and have our freedom.
Every weekend we’d head out in my Mum’s car. Me at the wheel driving up and down the hills. Practicing. They’d be cursing. Much telling off. Words of encouragement. A few near scrapes. However he persisted. With all of us. Until we passed.
He may have needed a stiff drink or several when we got home.
My Dad also taught my Great Auntie May who at the age of 63 sadly lost her husband. He left behind his car and so that she could have her freedom and retain some independence she decided rather than sell it she would learn to drive. So she did. This was in the 1970’s.
During the recent summer holidays my Mum and I took my niece Boo to see Mumma Mia at their local cinema. My Dad drove us into the nearby town where they live. On the way there we told Boo that this is where Grandad taught Nanny, Mummy and me to drive.
And I will do everything in my power to ensure she has hers too.
Newer PostSociety Says Yes Be Yourself. Just Not Like That.
Older PostChange is Inevitable. Growth is Intentional.

industry_corpus2: Others


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And when baby can sit up, move the toy bar to a 45 degree angle to create a cute car dashboard (complete with fuzzy die and a skunk air freshener that’s really vanilla scented!). Now, the steering wheel activates fun car sounds. And when your little driver puts the brakes on for a nap or bedtime, toss the soft large mat in the washer to be ready for the next road trip!
3 ways to play that grow with baby!
Tummy Time — Help baby cruise through tummy time by lowering the toy bar to the floor. Touching the steering wheel provides fun tune rewards!
Colorful hanging activities and variety of music and sound effects offer visual, tactile, and auditory stimulation.


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CASTLETON—The Vermont Fish & Wildlife program to introduce the new Birdseye Wildlife Management Area was well attended despite the fierce windstorm the night before, Friday, May 5, that knocked out power from Clarendon to Pittsford and caused extensive tree damage throughout the area. The event was held at the Kehoe Conservation Camp on Point of Pines Road in Bomoseen, where a spectacular view of the new WMA could be enjoyed from the outdoor deck. Inside, participants munched on vegetable and fruit finger food, crackers and cheese provided by the Conservation Fund.
Mark Scott, director of wildlife, opened the proceedings by describing the new WMA, which expands the preexisting Bird Mountain WMA to a total of approximately 4,000 acres within the towns of Ira and Poultney and is now christened Birdseye Wildlife Management Area. It is the second largest intact habitat block in the Taconics, yet is close to Rutland’s bustling city life. A slide show of the landscape and wildlife supplemented the talks.
Scott then introduced the commissioner of Vermont Fish & Wildlife, Louis Porter, a Vermont native and outdoorsman. Porter said Vermont is “in the restoration business” for species that had disappeared from Vermont in the past such as the whitetail deer and wild turkeys. He praised the Fish & Wildlife staff as well as the board for their important work, and expressed appreciation for the excellent relationship with U.S. Fish & Wildlife.
The new secretary of the Agency of Natural Resources, Julie Moore, told the group that Vermont is an important link in the wildlife corridor for the Northeast region and that ecological connectivity is essential to biodiversity on a regional as well as a local scale.
Nancy Bell, director of the Conservation Fund, which provided the intermediary step in the purchase of the acreage, then took the podium and expressed her heartfelt gratitude to both the Fish & Wildlife department and the towns of Ira and Poultney for this accomplishment.
Bell said this is a story about rocks and people. She had brought samples of bedrock to decorate the tables, and briefly referenced the tectonic movements that created the Taconic bedrock, which over the ages has given sustenance to the natural communities here.
The human communities of Ira and Poultney, she said, were “spirited, hardheaded and bighearted” and demonstrated their commitment to conservation at every level in the face of a lengthy resistance to a massive industrial wind project that would have crowned the ridgelines with a row of giant turbines. She acknowledged that it was a “challenge for the towns to consider state ownership,” and said the support of the select boards and the planning commissions was critical to public involvement and backing of the proposal.
Bell then presented framed prints in appreciation to Paul Donaldson, town manager of Poultney, Larry Taggart, former Select Board member of Ira, and Annette Smith, the nemesis of Big Wind, who helped the towns avoid certain ecological disaster.
She introduced Karen Freeman, conservation director with the Vermont Housing and Conservation Board, and Donald Campbell, Southwest director of the Vermont Land Trust. Both organizations are now co-holders of the comprehensive conservation easement for the WMA.
She also expressed thanks to Justin Lindholm, Green Mountain Power, and the townspeople of Tinmouth, Middletown Springs and West Rutland.
After the program a small group ventured out to visit the site, led by Justin Lindholm and F&W personnel including Jane Lazorchak, land acquisition and stewardship coordinator. In addition to viewing the cliffs where peregrine falcons nest, the group visited the Flynn cellar hole, home of the grandparents of a member of the group. Lindholm’s intimate knowledge of the area as a prior landowner on Bird Mountain added immeasurably to the experience for all.
Justin Lindholm (right center), former F&W board member, interprets the new WMA for participants who hiked up to Bird Mountain.

industry_corpus2: Agriculture & Fisheries


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A cork-wrapped platform and adjustable ankle strap could easily elevate our Scarlett wedge sandals to your instant favorite this season. Though Scarlett has a 4 1/2” wedge heel, its 1 1/4” platform provides the feeling of a 3 1/4” wedge heel.
Haven’t worn these yet, but super cute on your feet. They run true to size and I love the silver vs. gold every other brand uses.


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First published at 05:49 UTC on March 13th, 2019.
The Gambino Crime Family Boss was knocked off today. In this episode, I'll talk about the mafia and tell stories about my grandfather's fight against gangsters and the mob in the 1950s.

industry_corpus2: Film & Entertainment


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Consumer champion who got his break presenting inserts for Watchdog. That led to his own spin-off Rogue Traders, and latterly he can found presenting all manner of consumer affairs formats for the BBC. And of course the occasional game show.
In recognition of his work on consumer affairs programmes, in 2016 he became the inaugural recipient of the Media Hero Award from the Chartered Trading Standards Institute.

industry_corpus2: Media & Journalism


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RNS was formed to meet the needs of public sector bodies wishing to develop Public Service Network (PSN) and Next Generation Broadband networks who require informed, impartial advice and assistance.
© Copyright RNETSO 2011. All rights reserved.

industry_corpus2: Computing & Telecommunications


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George Jason Blythe “The Dawn of Kittrell”, age 55 of Murfreesboro, TN. passed away on Sunday, January 27, 2019.
He was preceded in death by his parents: George Edgar and Minnie Johnnie Ferrell Blythe, and a sister: Kimberly Blythe.
He is survived by his daughters: Ashley Blythe-Kuprion, Amber (Kassidy) Spence, grandchildren: Gage Kuprion, Karson Spence, Kingston Spence.
Visitation will be held at Murfreesboro Funeral Home on Tuesday, January 29, 2019 from 4pm – 8pm. Services will be held Wednesday, January 30, 2019 at 12pm with John Smith officiating.


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There are ongoing plans for a massive TV screen in Gloucester’s King’s Square. If the proposal is approved, Gloucester city centre can receive a giant present for its residents.
The TV screen is estimated around 30sqm and would pivot and rotate around. Though it will cost the region £100,000, people will be able to view important events like Royal Weddings and other major sporting events, from the Olympics, Wimbledon, Rugby World Cup, to football matches being broadcasted in the city centre.
Earlier this year, crowds watched Prince Harry and Meghan Markle get married and the FA Cup final was also shown as a testing ground for a larger, more permanent fixture in front of Iceland and nearby to the recently launched public toilets.
Plans for the TV screen have been submitted since May, but have only been validated in the past week weeks after archeological surveys were completed.
A final decision on the project by planning bosses will be made on Monday, December 17.


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Most organisations experience seasonality in their operations. It may be just holiday times or varying days in the management reporting calendar, but with some it can be more extreme, for example, firework manufacturers, ice cream producers, winter weather, Christmas or ‘Black Friday’. How do you reflect this in your performance measures?
Take the financial reports produced every month (or whichever other period you utilise), in these cases each management account (MA) will report the month's result and the year to date. The month concerned may, or may not, be benefiting from seasonality, and the cumulative result will cover a different period every month (from one to 12 months as the financial year progresses). How do your managers draw meaningful conclusions each month from this inconsistent information? You may be tempted to say comparisons with budgets, but we all know how long the detail of a budget remains relevant, many are out of date even before a financial year begins, let alone 12 months in. In addition. as the year progresses, the only line on a budget that remains relevant to stakeholders is the final result; do your senior managers not first turn to the bottom line when you present them with the monthly P&L? Nor will budget comparisons at the end of each month tell you whether your figures are improving or not, and they certainly do not consider all the varying unforeseen factors and interactions that have affected the organisation since the budget was prepared.
Many non-financial measures (NFPIs) are not immune to this seasonality problem either. NFPIs came into their own during the era of Kaizen (some may call it Continuous Improvement) two or three decades ago. Kaizen is an approach to work that systematically seeks to achieve small, incremental changes in processes in order to improve efficiency, quality and costs. NFPIs must therefore also show whether the subject of the measure is getting better or worse and, where appropriate, should pay attention to seasonality.
It is not difficult to reflect seasonality in your measures, just present them in the form of a 12 month rolling total or an average. Not only will this provide a seasonally adjusted measure, it will tell you whether profits are getting better or worse, and identify the rate at which this is happening. Include your budgets and forecasts/targets on any graphical representation of the measure and all will be seasonally adjusted and offer a complete picture, literally, of where you have been and where you are going. Once you have done this, you will come to realise that your monthly result is no guide to your success or failure and that ‘Only Trends Matter’.

industry_corpus2: Finance & Economics


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What was supposed to be a celebration of Beanie Sigel’s 35th birthday turned into a near deadly shooting that left one man critically injured.
On Saturday (March 7), Sigel (Dwight Grant) held his party in Penn’s Landing at Club Solo.
The event drew nearly 600 partygoers, and according to Philadelphia authorities Sigel’s mother handled admission duties at the club’s entrance.
Because of the Philly emcee’s previous criminal record, officials from the Department of Licenses/Inspections and the Pennsylvania State Police Bureau of Liquor Control Enforcement conducted a venue safety search at 10PM.
The shooting occurred later that evening at 1:35AM, when 24 year old Tyheem Baker of Camden, New Jersey was shot in the chest after coming out of Club Solo’s bathroom stall.
The shooting reportedly followed an argument the victim had with two unidentified men. Baker is currently listed in stable condition.
According to Sigel attorney Fortunato Perri Jr, his client was performing on stage at the time of the crime, and has no knowledge of the shooting or the perpetrators.
At press time, the venue is being investigated for its adherence to proper weapon searches and carding of patrons.
Last March, Sigel was sentenced to three months in prison for a third probation violation. The conviction was handed down following Sigel’s positive testing for illegal drugs.
Per an agreement with the courts, Sigel underwent drug treatment in order to maintain a 12-month supervised release.
At press time, Beanie Sigel could not be reached for comment.
It’s always something, y’all. It looks like it’s never gonna stop either.

industry_corpus2: Law & Justice


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You've taught me something. Thanks for sharing.
I have just the spot to try this. Maybe the blue plate attracts them too.
I seldom have a butterfly on my flowers. Maybe I should try this. Never would have thought of it.
We would like to add your blog to the Top Food Blog list in www.mytaste.ph/ . Your blog is impressively BEAUTIFUL and it deserves to be included on the Top list!! Great recipes!! We will feature your blog and we will make a lot of shout out about your recipes on our fan pages so that people and our 4million users worldwide will be able to check it on our site.

industry_corpus2: Hospitality & Catering


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Violet Town Bush Community Service provides Level 1-4 Home Care Packages. The Program aims to support frail older people to stay in their own homes as along as possible maintaining their safety and independence, based upon the principles of Consumer Directed Care.
to enable consumers to have choice and flexibility in the way that the consumers’ aged care and support is provided at home.
Our goal is to work with consumers and their families in developing a suite of services that meet their needs. Through a process of assessment and consultation we work with you to determine what your priorities are and provide a flexible range of services to meet your needs.
Working in partnership with our Colleagues at the Strathbogie Shire, Euroa Health and Nagambie Healthcare we can ensure services are local and prompt.

industry_corpus2: Health & Medicine


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S&L Podcast - #95 - Have You Seen This Direwolf?
We're all giddy about our new video show at Geek and Sundry, but we promise there's more to the episode than just that. Though if you have questions about what the video show means, hopefully loads of them are answered right off the top of the show. We also dig into Lies of Locke Lamora (though we don't wrap it up quite yet) and help save SciFi. Literally.
Sword & Laser coming to video!
Yes we know what the next book will be - and yes we know it's not a laser, but the book after that will be and we need your help picking it!
If made into a movie, who would you cast?
Finally a real Prometheus trailer and not just a teaser!
SF Signal is doing Lies of Locke Lamora too!
The Lies of Locke Lamora > A Protagonist in Need of a Want?
The Lies of Locke Lamora > Why isn't there a map?
I had the honor of getting to see Tom and Veronica at the WonderCon signing this Saturday. Tom gave me a shirt and I thought it was just an XL when he gave it to me, but was elated to see it was an XXXL when I checked it later. I'm so used to free giveaways being so small on me and most people overlook us big boys. I'm a big fan of all that you and I can't thank you enough.
I'm very excited about your video podcast, and all teh geek and sundry goodness coming. But I have one concern: Is there a 'what we're drinking' section? If there is no drinking to begin the show, it can't really be an S&L podcast, can it?
Well it's an amazing kick-off to a great fantasy novel, but Tom can't stop himself from embarassing admissions, and Veronica is shocked into speechlessness. So it's that kind of episode.
2011 Nebula Awards Nominees Announced Thanks David!
Updates on Blue Remembered Earth and The Coldest War.
I've been catching up on a few weeks of podcasts, so feel free to ignore this if you've moved on from the ""is listening to an audiobook really reading?"" issue.
Anyway, from a scientific perspective, all the claims that brain handles audio differenetly from the written word are true but entirely meaningless to this debate.
The problem is that unless you have some well-formed argument about what a difference in neural patterns signfiies, its meaningless to base any claim by stating simply that the ""brain handles x differnetly from y"". The reason for this is that, at some level, the brain handles nearly everything differently from everything else.
Point being: saying that brain activity is different when listening vs. ""reading"" tells us nothing particularly useful.
Do people remember the text better when it is read to them vs. when they read it themselves?Are details remembered better?Does the author intent come through better in one medium vs. another? Are people more likely to ""skim"" in one medium vs. another?After some time do people forget how they ""read"" the book? (that is, years afterwards, is the content stored seperately from the delivery method).
These are actually answerable questions and it would be interesting if someone did this research. But I can say from my own experience that there are times when audio is clearly the ""better"" method. One obvious example, is that I know how to pronounce character names and places.
As a Wheel of Time fan, I can't wait, hope it doesn't get delayed but i respect the need to finish this off right.
Sword: The Lies of Locke Lamora by Scott Lynch.
Veronica, thanks for introducing me the Alex Craft series in your new book club, looking forward for more good stuff.
Lastly here is book rec I think you will both enjoy immensely but probably doesn't fit the book club profile, it takes place in a post Zombie outbreak world in which civilization didn't collapse largely thanks to bloggers and the lessons learned from George Romero! the book is called Feed by Mira Grant (Newsflesh Trilogy #1) it's a clever, intelligent book, just look at the cover.