Short-axis-mode rotation of a free rigid body by perturbation series

TL;DR

This paper develops a perturbation series method for analyzing the rotation of free rigid bodies near their principal axis of maximum inertia, simplifying calculations especially for nearly axisymmetric bodies like solar system planets.

Contribution

It introduces a Hamiltonian rearrangement and action-angle variables approach that improves upon classical methods for bodies rotating close to their principal axis.

Findings

The perturbation solution agrees with Kinoshita's expansions.

The method is advantageous for nearly axisymmetric bodies.

Applicable to solar system bodies with small triaxiality.

Abstract

A simple rearrangement of the torque free motion Hamiltonian shapes it as a perturbation problem for bodies rotating close to the principal axis of maximum inertia, independently of their triaxiality. The complete reduction of the main part of this Hamiltonian via the Hamilton-Jacobi equation provides the action-angle variables that ease the construction of a perturbation solution by Lie transforms. The lowest orders of the transformation equations of the perturbation solution are checked to agree with Kinoshita's corresponding expansions for the exact solution of the free rigid body problem. For approximately axisymmetric bodies rotating close to the principal axis of maximum inertia, the common case of major solar system bodies, the new approach is advantageous over classical expansions based on a small triaxiality parameter.