On the motion of Chaplygin's sledge
The plane motion of Chaplygin's sledge is studied. In his original studies of this non-holonomic system, Chaplygin assumed that the support plane is horizontal, and used a reduction factor to reduce the problem to the study of a Hamiltonian system with two degrees of freedom and one cyclical coordinate (i.e., a completely Liouville integrable system). A smooth reversible replacement of the phase variables is used below for the reduction. The motion is studied in detail by the methods of Hamiltonian mechanics, and the motion on an inclined plane is studied by the averaging method.
scientific article; zbMATH DE number 4087106