Slosh dynamics of a spin-stabilized spacecraft comprising off-axis tanks filled partially with liquid propellant

The fundamental nonlinear equations of motion were derived and the specialized to a steady-state rotation of the vehicle about a given axis of rotation. A thrust about the spin axis was introduced. A perturbation solution was derived which linearizes the problem. The effect of the centrifugal and coriolis accelerations together with vorticity are implicitly taken into consideration in the formulation. A variational formulation of the associated boundary conditions is presented. For practical cases it is shown that the simple classical pendulum representation for slosh is not very appealing for a spinning spacecraft unless severe restrictions are allowed.