Nonlinear attitude stability of a spacecraft on a stationary orbit around an asteroid subjected to gravity gradient torque

TL;DR

This paper extends the analysis of spacecraft attitude stability to stationary orbits around asteroids, using geometric mechanics and nonlinear stability methods, revealing new stability domains influenced by asteroid parameters.

Contribution

It introduces a geometric mechanics framework for analyzing nonlinear attitude stability of spacecraft around asteroids, deriving stability conditions in a generalized gravity gradient context.

Findings

Stability domains vary significantly from classical cases.

Nonlinear stability depends on asteroid shape parameters.

Intermediate-moment principal axis offers unique stability characteristics.

Abstract

The classical problem of attitude stability in a central gravity field is generalized to that on a stationary orbit around a uniformly-rotating asteroid. This generalized problem is studied in the framework of geometric mechanics. Based on the natural symplectic structure, the non-canonical Hamiltonian structure of the problem is derived. The Poisson tensor, Casimir functions and equations of motion are obtained in a differential geometric method. The equilibrium of the equations of motion, i.e. the equilibrium attitude of the spacecraft, is determined from a global point of view. Nonlinear stability conditions of the equilibrium attitude are obtained with the energy-Casimir method. The nonlinear attitude stability is then investigated versus three parameters of the asteroid, including the ratio of the mean radius to the stationary orbital radius, the harmonic coefficients C20 and C22. It is found that when the spacecraft is located on the intermediate-moment principal axis of the asteroid, the nonlinear stability domain can be totally different from the classical Lagrange region on a circular orbit in a central gravity field.