  The article considers Chaplygin sleigh on a plane in 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 quadratic, various behaviors are observed numerically
depending of the energy, from those characteristic to conservative dynamics
(regularity islands and chaotic sea) to strange attractors. This is another
example of nonholonomic system manifesting these phenomena (similar to those
for Celtic stone or Chaplygin top), which reflects a fundamental nature of
these systems occupying intermediate position between conservative and
dissipative dynamics.
