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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 551–559 (Mi nd682)  

Complex Dynamics in Generalizations of the Chaplygin Sleigh

S. P. Kuznetsov

Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: The article considers the Chaplygin sleigh on a plane in a potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a potential with rotational symmetry; in both cases the models reduce to four-dimensional differential equations conserving mechanical energy. Assuming the potential functions to be quadratic, various behaviors are observed numerically depending on the energy, from those characteristic to conservative dynamics (regularity islands and chaotic sea) to strange attractors. This is another example of a nonholonomic system manifesting these phenomena (similar to those for Celtic stone or Chaplygin top), which reflects a fundamental nature of these systems occupying an intermediate position between conservative and dissipative dynamics.

Keywords: Chaplygin sleigh, nonholonomic system, chaos, attractor

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
This work was supported by the Russian Science Foundation, grant No. 15-12-20035.


DOI: https://doi.org/10.20537/nd190414

Full text: PDF file (752 kB)
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MSC: 37J60, 37C10, 34C60, 34C28
Received: 28.05.2019
Accepted:05.08.2019

Citation: S. P. Kuznetsov, “Complex Dynamics in Generalizations of the Chaplygin Sleigh”, Nelin. Dinam., 15:4 (2019), 551–559

Citation in format AMSBIB
\Bibitem{Kuz19}
\by S. P. Kuznetsov
\paper Complex Dynamics in Generalizations of the Chaplygin Sleigh
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 551--559
\mathnet{http://mi.mathnet.ru/nd682}
\crossref{https://doi.org/10.20537/nd190414}


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