Speedup of a Chaplygin top by means of rotors

Borisov, A. V.; Kilin, A. A.; Пивоварова, Е. Н.

doi:10.31857/s0869-56524853285-289

Cited by 4 publications

(4 citation statements)

References 13 publications

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“…In recent studies of nonholonomic systems the problems of moving a Chaplygin sleigh and Chaplygin top by small periodic control actions are considered. The results confirm the possibility of constant acceleration (speedup) of the wheeled vehicle due to the periodic change in the mass distribution [1,2], as well as acceleration of the Chaplygin top with the help of an internal rotor [3]. In this case, the acceleration mechanism is called Fermi acceleration and is observed in systems with two and a half or more degrees of freedom.…”

Section: Introductionsupporting

confidence: 70%

The Dynamics of a Spherical Robot of Combined Type by Periodic Control Actions

Karavaev¹,

Kilin²

2019

Nelin. Dinam.

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This paper presents the results of the study of the dynamics of a real spherical robot of combined type in the case of control using small periodic oscillations. The spherical robot is set in motion by controlled change of the position of the center of mass and by generating variable gyrostatic momentum. We demonstrate how to use small periodic controls for stabilization of the spherical robot during motion. The results of numerical simulation are obtained for various initial conditions and control parameters that ensure a change in the position of the center of mass and a variation of gyrostatic momentum. The problem of the motion of a spherical robot of combined type on a surface that performs flat periodic oscillations is also considered. The results of numerical simulation are obtained for different initial conditions, control actions and parameters of oscillations.

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Section: Introductionsupporting

confidence: 70%

The Dynamics of a Spherical Robot of Combined Type by Periodic Control Actions

Karavaev¹,

Kilin²

2019

Nelin. Dinam.

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“…A proof of unbounded growth of energy under periodic oscillations of the rotor inside the Chaplygin sleigh and of bounded growth in the presence of dissipation is given in [7]. An unbounded acceleration for the Chaplygin sphere is discussed in [13]. We note that the acceleration mechanism of spheres is still not understood.…”

Section: Resultsmentioning

confidence: 99%

On the Chaplygin Sphere in a Magnetic Field

Borisov

Tsiganov

2019

Regul. Chaot. Dyn.

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We consider the possibility of using Dirac's ideas of the deformation of Poisson brackets in nonholonomic mechanics. As an example, we analyze the composition of external forces that do no work and reaction forces of nonintegrable constraints in the model of a nonholonomic Chaplygin sphere on a plane. We prove that, when a solenoidal field is applied, the general mechanical energy, the invariant measure and the conformally Hamiltonian representation of the equations of motion are preserved. In addition, we consider the case of motion of the nonholonomic Chaplygin sphere in a constant magnetic field taking dielectric and ferromagnetic (superconducting) properties of the sphere into account. As a by-product we also obtain two new integrable cases of the Hamiltonian rigid body dynamics in a constant magnetic field taking the magnetization by rotation effect into account.

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“…In this paper, we consider a dynamically asymmetric ball rolling without slipping, in which rotors rotate and pairs of internal material points move, so that the center of mass always coincides with the geometric center of the shell. Changing the moments of inertia of the body due to the motion of masses entails various effects [16]: the appearance of attracting sets and the appearance of strange attractors. Computer analysis of the resulting system dynamics and contact point trajectories is performed.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Chaplygin Ball with Variable Parameters

Borisov¹,

Mikishanina²

2020

Nelin. Dinam.

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This work is devoted to the study of the dynamics of the Chaplygin ball with variable moments of inertia, which occur due to the motion of pairs of internal material points, and internal rotors. The components of the inertia tensor and the gyrostatic momentum are periodic functions. In general, the problem is nonintegrable. In a special case, the relationship of the problem under consideration with the Liouville problem with changing parameters is shown. The case of the Chaplygin ball moving from rest is considered separately. Poincaré maps are constructed, strange attractors are found, and the stages of the origin of strange attractors are shown. Also, the trajectories of contact points are constructed to confirm the chaotic dynamics of the ball. A chart of dynamical regimes is constructed in a separate case for analyzing the nature of strange attractors.

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Speedup of a Chaplygin top by means of rotors

Cited by 4 publications

References 13 publications

The Dynamics of a Spherical Robot of Combined Type by Periodic Control Actions

The Dynamics of a Spherical Robot of Combined Type by Periodic Control Actions

On the Chaplygin Sphere in a Magnetic Field

Dynamics of the Chaplygin Ball with Variable Parameters

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