Secular solution for delta-V during spin rate change maneuvers of rigid body spacecraft

Abstract

Analytic expressions have been found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions have been used to solve for the secular terms in the translational delta-V equations in inertial space. This secular delta-V solution is of interest in application to spinning spacecraft in that it describes the average direction of the delta-V of the spacecraft during a spin-up maneuver. Numerical integration of the governing differential equations has verified that the secular delta-V solution is valid for large time and is accurate in many physical situations including spin-up maneuvers of the Galileo spacecraft.