Solvable cases in the problem of motion of a heavy rotationally symmetric ellipsoid on a perfectly rough plane

摘要

We consider a classical problem of nonholonomic system dynamics - the problem of motion of a rotationally symmetric body on a fixed perfectly rough plane in a case when the moving body is a rotationally symmetric ellipsoid. Using the Kovacic algorithm we found several conditions under which equations of motion of the ellipsoid can be completely solved in quadratures.