Generalizations of the Kovalevskaya case and quaternions

TL;DR

This paper explores advanced reduction schemes in rigid body dynamics, leading to new generalizations of the Kovalevskaya case on e(3) and connecting to earlier proposed singular terms.

Contribution

It introduces novel reduction methods that extend the Kovalevskaya case to e(3) and clarifies their relation to previously proposed singular terms.

Findings

New generalizations of the Kovalevskaya case to e(3)

Identification of reduction schemes that produce singular additive terms

Enhanced understanding of rigid body dynamics reductions

Abstract

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