Transformations of mechanical systems with cyclic coordinates and new integrable problems (Q2773150)

The author studies some integrable cases in rigid body dynamics. As is known, in many problems of mechanical interest a particular integrable case can be generalized to an integrable case for arbitrary initial conditions. Here four new integrable cases are obtained as generalizations of known cases, by including certain additional combinations of gravitational and electromagnetic forces. A direct verification of the constancy of the first integrals is possible using the equations of motion. The author also discusses explicit time solutions of these new cases, and gives for two cases an interesting mechanical interpretation.