Dynamics of a Balanced Truncated Rubber Ellipsoid of Revolution

This paper addresses the problem of the motion a balanced ellipsoid of revolution with symmetrically truncated vertices that rolls without slipping on a plane. First integrals are found and reduction to quadratures is performed. Partial solutions to the resulting system are found. Using an analysis of bifurcation curves, bifurcations of partial solutions are investigated and a classification of all types of bifurcation diagrams depending on parameters is carried out.