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This article is cited in 7 scientific papers (total in 7 papers)
A Nonholonomic Model of the Paul Trap
Alexey V. Borisovab, Alexander A. Kilinc, Ivan S. Mamaevd a Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
b A. A. Blagonravov Mechanical Engineering Research Institute of RAS, ul. Bardina 4, Moscow, 117334 Russia
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
d Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia
Abstract:
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 Poincaré 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.
Keywords:
Paul trap, stability, nonholonomic system, three-dimensional map, gyroscopic stabilization, noninertial coordinate system, Poincaré map, nonholonomic constraint, rolling without slipping, region of linear stability.
Received: 12.03.2018 Accepted: 16.04.2018
Citation:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Nonholonomic Model of the Paul Trap”, Regul. Chaotic Dyn., 23:3 (2018), 339–354
Linking options:
https://www.mathnet.ru/eng/rcd327 https://www.mathnet.ru/eng/rcd/v23/i3/p339
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Abstract page: | 215 | References: | 36 |
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