New solvable problems in the dynamics of a rigid body about a fixed point in a potential field

TL;DR

This paper identifies new solvable cases in the dynamics of a rigid body about a fixed point under specific potential fields, providing explicit solutions and generalizations of classical problems.

Contribution

It determines the potential forms allowing constant angular velocity in a principal inertia plane and introduces a multi-parameter generalization of classical solutions.

Findings

Explicit solutions reduce to single integral inversion.

Generalized classical cases with elliptic and ultraelliptic solutions.

New solvable potentials for rigid body dynamics.

Abstract

We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the problem of motion is reduced to inversion of a single integral. A several-parameter generalization of the classical case due to Bobylev and Steklov is found. Special cases solvable in elliptic and ultraelliptic functions of time are discussed.