An inhomogeneous Chaplygin sleigh (Q1701462)

The authors consider the inertial dynamics of an inhomogeneous Chaplygin sleigh. An immediate generalization of this problem is the investigation of the motion of the sleigh in a gravitational field on an inclined plane. In the case of a homogeneous constraint, this system is not integrable and exhibits complex asymptotic behavior. The authors present a new first integral, which is an immediate generalization of the energy integral. This integral is not obvious, since, generally speaking, in the case of inhomogeneous constraints the energy integral does not exist. Explicit solution, are obtained and some trajectories are constructed explicitly.