Analytic classification of singularities in the generalized Kowalevski case

TL;DR

This paper analytically classifies all critical points of the momentum map in the Kowalevski top problem with two constant fields, advancing understanding of its singularities.

Contribution

It provides a complete analytical classification of singularities in the generalized Kowalevski case, which was previously not fully understood.

Findings

All critical points of the momentum map are classified.

The types of singularities are explicitly determined.

The results enhance the integrable systems theory for rigid body dynamics.

Abstract

In the problem of motion of the Kowalevski top on two constant fields (the A.G.Reyman - M.A.Semenov-Tian-Shansky case) the type of all critical points of the momentum map is calculated.