Fully-coupled spherical modular pendulum model to simulate spacecraft propellant slosh

A spacecraft undergoing general translational and rotational motion can be affected by the sloshing of propellant. A spherical pendulum model is used for simulating this phenomenon because it can better represent the sloshing behavior for rotational dynamics in micro-gravity. This paper develops the fully coupled equations of motion of such a system and presents the solution in a form suitable for the back-substitution method. This modular formulation permits the use of as many pendulums as necessary to approximate the actual sloshing behavior. The general formulation makes minimal assumptions for the rigid portion of the spacecraft and is developed in a frame independent manner making the model applicable to wide range of spacecraft configurations. The model is implemented and verified using energy and momentum conservation in the Basilisk astrodynamics software package. The results of a simulation example of a GPS satellite are shown as an application of the model.