Chaplygin Top with a Periodic Gyrostatic Moment
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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.
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- 2.I. A. Bizyaev, A. V. Borisov, V. V. Kozlov, and I. S. Mamaev, “Fermi-Like Acceleration and Power-Law Energy Growth in Nonholonomic Systems,” submitted to Nonlinearity.Google Scholar
- 19.K. M. Ehlers and J. Koiller, “Rubber Rolling: Geometry and Dynamics of 2 - 3 - 5 Distributions,” in Proc. IUTAM Symposium 2006 on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, Russia, 25–30 August 2006), pp. 469–480.Google Scholar