In this paper we investigate a nonholonomic system with parametric excitation,
a Roller Racer with variable gyrostatic momentum. We examine in detail the problem of the
existence of regimes with unbounded growth of energy (nonconservative Fermi acceleration).
We find a criterion for the existence of trajectories for which one of the velocity components
increases withound bound and has asymptotics $t^{1/3}$. In addition, we show that the problem
under consideration reduces to analysis of a three-dimensional Poincaré map. This map exhibits
both regular attractors (a fixed point, a limit cycle and a torus) and strange attractors.
Keywords:
nonholonomic mechanics, Roller Racer, Andronov – Hopf bifurcation, stability, central manifold, unbounded speedup, Poincaré map, limit cycle, strange attractor
Citation:
Bizyaev I. A., Mamaev I. S., Roller Racer with Varying Gyrostatic Momentum: Acceleration Criterion and Strange Attractors, Regular and Chaotic Dynamics,
2023, Volume 28, Number 1,
pp. 107-130