  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.
