The eccentric case of a fast-rotating, gravity-gradient-perturbed satellite attitude solution

摘要

A closed-form first-order perturbation solution for the attitude evolution of a triaxial space object in an elliptical orbit is presented. The solution, derived using the Lie-Deprit method, takes into account gravity-gradient torque and is facilitated by an assumption of fast rotation of the object. The formulation builds on the earlier implementation of Lara and Ferrer, which assumes a circular orbit. The previously presented workwhich assumes spin about an object's axis of maximum inertiais further extended by the explicit presentation of the transformations required to apply the solution to an object spinning about its axis of minimum inertia. Additionally, several numerical analyses are presented to more completely assess the utility of the solution. These studies (1) validate the elliptical solution, (2) assess the impact of varying the small parameter of the perturbation procedure, (3) analyze the assumption of fast rotation, and (4) apply the solution to the common and important scenario of a tumbling rocket body.