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

Abstract

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.