Complex Dynamics in Generalizations of the Chaplygin Sleigh
S. P. Kuznetsov
Udmurt State University,
ul. Universitetskaya 1, Izhevsk, 426034 Russia
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.
Chaplygin sleigh, nonholonomic system, chaos, attractor
|Russian Science Foundation
|This work was supported by the Russian Science Foundation, grant No. 15-12-20035.
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MSC: 37J60, 37C10, 34C60, 34C28
S. P. Kuznetsov, “Complex Dynamics in Generalizations of the Chaplygin Sleigh”, Nelin. Dinam., 15:4 (2019), 551–559
Citation in format AMSBIB
\by S. P. Kuznetsov
\paper Complex Dynamics in Generalizations of the Chaplygin Sleigh
\jour Nelin. Dinam.
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