Solvable Cases in the Problem of Motion of a Heavy Rotationally Symmetric Ellipsoid on a Perfectly Rough Plane

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.