Regular and chaotic attractors in the nonholonomic model of Chapygin’s ball. (Russian. English summary) Zbl 1352.70039
The movement without slippage of inhomogeneous ball on a horizontal plane under influence of gravity is studied in this work. With the help of analytical and numerical methods of nonlinear dynamics, it is shown that at certain parameter values the unbalanced inhomogeneous ball changes (reverses) the direction of rotation to opposite. Besides, figure-eight attractor related to the real strange attractors of pseudo-hyperbolic type is discovered.
Reviewer: Gasanbek T. Arazov (Baku)
MSC:
70F25 | Nonholonomic systems related to the dynamics of a system of particles |
70E18 | Motion of a rigid body in contact with a solid surface |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37G35 | Dynamical aspects of attractors and their bifurcations |