The problem on a motion of a heavy rigid dynamically symmetric body, bounded by a surface of rotation, on a fixed horizontal plane without sliding is considered. In a case, when the bounded surface satisfies to certain condition, the explicit form of two first integrals of equation of motion of a body, in addition to the energy integral is found. These integrals are linear with respect to generalized velocities. This work supplements and develops results, received in classical work.

Theoretical and applied problems of mechanics