Volume 132, Number 2, October 2020
|Number of page(s)||7|
|Published online||23 December 2020|
Chaplygin sleigh in the quadratic potential field
1 Saratov Branch Kotel'nikov Institute of Radioengineering and Electronics of RAS - Saratov, Russia
2 Steklov Mathematical Institute of RAS - Moscow, Russia
3 Yuri Gagarin State Technical University of Saratov - Saratov, Russia
Received: 10 July 2020
Accepted: 25 September 2020
We study numerically the dynamics of Chaplygin sleigh under the action of the quadratic potential field. In contrast with the free Chaplygin sleigh our mechanical model manifests a complex behaviour: conservative-like chaotic regimes at low energies, coexistent pairs of chaotic attractors and repellers, mapping to each other by time-reversal symmetry, and the recently discovered phenomenon of attractor and repeller intersection, at high energies. We demonstrate that the development of attractors and repellers corresponds to a period doubling scenario, followed by their collision and instant increase in size.
PACS: 05.45.-a – Nonlinear dynamics and chaos / 45.40.-f – Dynamics and kinematics of rigid bodies
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