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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33408There 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.17 pages, AMS-LaTeXDifferential GeometryNew families of conservative systems on $S^2$ possessing an integral of fourth degree in momentatext