2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76541The aim of this paper is to describe a class of conservative systems on $S^2$ possessing an integral cubic in momenta. We prove that this class of systems consists off the case of Goryachev-Chaplygin, the one-parameter family of systems which has been found by the author in the previous paper (dg-ga/9711005) and a new two-parameter family of conservative systems on $S^2$ possessing an integral cubic in momenta.16 pages, LaTexDifferential Geometry58F07text