Short-axis-mode rotation in complex variables

TL;DR

This paper introduces a method for analyzing short-axis-mode rotation of rigid bodies using complex variables, simplifying the integration process and enabling efficient handling of perturbations without elliptic functions.

Contribution

It presents a novel approach that transforms the torque-free motion integration into polynomial algebra, simplifying calculations and extending to gravity-gradient perturbations.

Findings

Simplifies rigid body rotation integration using complex variables.

Avoids elliptic functions in the solution process.

Can handle gravity-gradient perturbations near the axis of maximum inertia.

Abstract

Decomposition of the free rigid body Hamiltonian into a "main problem" and a perturbation term provides an efficient integration scheme that avoids the use of elliptic functions and integrals. In the case of short-axis-mode rotation, it is shown that the use of complex variables converts the integration of the torque-free motion by perturbations into a simple exercise of polynomial algebra that can also accommodate the gravity-gradient perturbation when the rigid body rotation is close enough to the axis of maximum inertia.