Analytical model for momentum transfer of spacecraft containing liquid

A study was conducted to demonstrate an analytic model to determine minimum wheel torques achieving turnover and desired maneuver times. The new model included propellant slosh and product of inertia terms to determine the wheel speed and acceleration for a given spacecraft configuration when the initial and steady-state body rates and the steady-state time were predetermined. It also determined the turnover wheel speed and corresponding time by incorporating the angular momentum of the initial and final spin axes. The analytical model was compared with numerical simulations to demonstrate its accuracy and appropriateness. The physical model consisted of a spacecraft main body, a momentum wheel, and a liquid fuel tank, while the model for the spinning spacecraft used an equivalent pendulum for the slosh mass. The derived analytical solutions were also verified through comparisons to numerical solutions and agreed to a certain degree.