New families of conservative systems on $S^2$ possessing an integral of fourth degree in momenta

Abstract

There is a well-known example of integrable conservative system on $S^2$, the case of Kovalevskaya in the dynamics of a rigid body, possessing an integral of fourth degree in momenta. Goryachev proposed a one-parameter family of examples of conservative systems on $S^2$ possessing an integral of fourth degree in momenta which includes the case of Kovalevskaya. In this paper we proposed new examples of conservative systems on $S^2$ possessing an integral of fourth degree in momenta.