One class of solutions with two invariant relations for the problem of motion of the Kowalevski top in double constant field

TL;DR

This paper introduces a new integrable case of the Kowalevski top in a double constant field, characterized by two invariant relations, extending classical results and generalizing known classes of motion.

Contribution

It presents a novel integrable case with two invariant relations for the Kowalevski top in a double field, expanding the set of known solutions.

Findings

New integrable case with two invariant relations

Generalization of 2nd and 3rd Appelrot classes

Reduction to classical cases when one field vanishes

Abstract

Consider a rigid body having a fixed point in a superposition of two constant force fields (for example, gravitational and magnetic). Introducing the condition of Kowalevski type, O.I.Bogoyavlensky (1984) has found the first integral generalizing that of Kowalevski and pointed out the integrable case with two invariant relations, which reduces to the 1st Appelrot class when one of the fields vanishes. The article presents a new case with two invariant relations integrable in Jacobi sense and generalizing the 2nd and 3rd classes of Appelrot.