A Nonholonomic Model of the Paul Trap

作者：Borisov Alexey V^*; Kilin Alexander A; Mamaev Ivan S

来源：Regular & Chaotic Dynamics, 2018, 23(3): 339-354.

DOI：10.1134/S1560354718030085

• Paul trap
• stability
• nonholonomic system
• three-dimensional map
• gyroscopic stabilization
• noninertial coordinate system
• Poincare map
• nonholonomic constraint
• rolling without slipping
• region of linear stability

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, 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.

• 出版日期2018-5