Date of Award


Document Type


Degree Name

Master of Science in Mechanical Engineering (MSME)


Mechanical Engineering

First Advisor

Dr. Mohammad A. Ayoubi


We use Kane’s method to present the equations of motion of a spinning spacecraft with three momentum wheels, a nutation damper, and a spherical pendulum. The spherical pendulum is adopted as a simple mechanical equivalent of fuel sloshing in partially-filled tanks. The proposed model is an extension of the existing model in the literature. We verify and validate our model for two cases: flat spin and a simple reorientation maneuver. Numerical simulations are in agreement with existing results in the literature.

Errors in proper orientation of a desired velocity vector of a thrusting, spinning spacecraft are caused by thrust misalignment of various kind. We use a trapezoidal thrust scheme to reduce the error in a spacecraft with fuel sloshing. Equations of motion of the system are derived using Kane’s method accounting time-vary moment of inertia, torque and mass with planar and spherical pendulums models of fuel slosh that are the most accurate mechanical equivalent models available in the literature. Comparison between the Star 48B thrust scheme and proposed trapezoidal thrust scheme are proposed with optimizing the trapezoidal thrust scheme in order to minimize the average velocity pointing error. Simulation results for an existing simple thrusting rigid body model confirm the accuracy of our model.