  Generalizations of the Kovalevskaya, Chaplygin, Goryachev-Chaplygin and
Bogoyavlensky systems on a bundle are considered in this paper. Moreover, a
method of introduction of separating variables and action-angle variables is
described. Another integration method for the Kovalevskaya top on the bundle is
found. This method uses a coordinate transformation that reduces the
Kovalevskaya system to the Neumann system. The Kolosov analogy is considered. A
generalization of a recent Gaffet system to the bundle of Poisson brackets is
obtained at the end of the paper.
