Generalizations of the Kovalevskaya case and quaternions

This paper provides a detailed description of various reduction schemes in rigid body dynamics. The analysis of one of such nontrivial reductions makes it possible to put the cases already found in order and to obtain new generalizations of the Kovalevskaya case to $e(3)$. Note that the indicated reduction allows one to obtain in a natural way some singular additive terms that were proposed earlier by D. N. Goryachev.