Nonexistence of liouvillian solutions in the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough plane

Abstract

We consider the classical problem of nonholonomic system dynamics the problem of motion of a rotationally symmetric ellipsoid on a fixed perfectly rough horizontal plane. It is well known that the solution of this problem is reduced to the integration of the second order linear differential equation with respect to r the projection of the angular velocity of the ellipsoid onto its axis of symmetry. Using the Kovacic algorithm we prove the nonexistence of liouvillian solutions for the corresponding second order linear differential equation for almost all values of parameters of the problem. The paper is organized as follows. After the introductory paragraph, in the second paragraph we briefly discuss the Kovacic algorithm for solving the second order linear differential equation. In the third paragraph we apply this algorithm to the problem of motion of a rotationally symmetric ellipsoid on a perfectly rough horizontal plane and prove the nonexistence of liouvillian solutions in the considered problem. Refs 4.