A new integrable problem with a quartic integral in the dynamics of a rigid body

TL;DR

This paper introduces a new integrable case in the dynamics of a rigid body with potential and gyroscopic forces, extending previous models and providing physical interpretations involving electromagnetic interactions.

Contribution

It presents a novel integrable problem with a quartic integral, generalizing earlier models and applicable to physically interpretable forces.

Findings

New integrable case with quartic integral identified

Generalizes Chaplygin and Yehia's rigid body motion models

Involves physically interpretable potential and gyroscopic forces

Abstract

We consider the problem of motion of a rigid body about a fixed point under the action of an axisymmetric combination of potential and gyroscopic forces. We introduce a new integrable case, valid on zero level of the cyclic integral, that generalizes the known case of motion of a body in liquid due to Chaplygin and its subsequent generalization by Yehia. Apart from certain singular potential terms, the new case involves finite potential and gyroscopic forces, which admit physical interpretation as resulting from interaction of mass, magnetized parts and electric charges on the body with gravitational, electric and magnetic fields.