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This article is cited in 2 scientific papers (total in 2 papers)
Roller Racer with Varying Gyrostatic Momentum:
Acceleration Criterion and Strange Attractors
Ivan A. Bizyaeva, Ivan S. Mamaevb a Ural Mathematical Center, Udmurt State University,
ul. Universitetskaya 1, 426034 Izhevsk, Russia
b Kalashnikov Izhevsk State Technical University,
ul. Studencheskaya 7, 426069 Izhevsk, Russia
Abstract:
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.
Received: 07.11.2022 Accepted: 27.12.2022
Citation:
Ivan A. Bizyaev, Ivan S. Mamaev, “Roller Racer with Varying Gyrostatic Momentum:
Acceleration Criterion and Strange Attractors”, Regul. Chaotic Dyn., 28:1 (2023), 107–130
Linking options:
https://www.mathnet.ru/eng/rcd1197 https://www.mathnet.ru/eng/rcd/v28/i1/p107
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Abstract page: | 133 | References: | 31 |
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