Complex Dynamics in Generalizations of the Chaplygin Sleigh
2019, Vol. 15, no. 4, pp. 551-559
Author(s): Kuznetsov S. P.
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.
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