Dynamics of a variable mass system applied to spacecraft rocket attitude theory

This research project is a study of the dynamics of a variable mass system. The scope of this research project is to gain understanding as to how a variable mass system will behave. The intent is to bring the level of understanding of variable mass dynamics higher and closer to the level of constant mass dynamics in the area of spacecrafts in particular. A main contribution is the finding of a set of criteria to minimize or eliminate the deviation of the nutation angle (or cone angle or angle of attack) of spacecraft rockets passively, i.e. without active control. The motivation for this research project is the Star 48 anomaly. The Star 48 is a solid rocket motor which has propelled (boosted) communication satellites from lower earth orbit to a higher one during the 1980's. The anomaly is that when the spacecraft rocket is being propelled, the nutation angle may deviate excessively which is considered undesirable.; In the first part of this research project, a variable mass system is described and defined and the governing equations are derived. The type of governing equations derived are those that are most useful for analyzing the motion of a spacecraft rocket. The method of derivation makes use of Leibnitz Theorem, Divergence Theorem and Newton's Second Law of Motion.; Next, the governing equations are specialized with several assumptions which are generally accepted assumptions applied in the analysis of spacecraft rockets. With these assumptions, the form governing equations is discussed and then the equations are solved analytically for the system's angular velocity.; Having solved for the angular velocity of the system, the attitude of the system is obtained using a unique method which circumvents the nonlinearities that exist using Euler Angles and their kinematical equations. The attitude is approximately found analytically and a set of criteria is discussed which will minimize or eliminate the deviation of the nutation angle of a spacecraft rocket.; Finally, an interesting scalar equation and vector equation is presented which sheds some light on the motion of a spacecraft rocket. The vector equation allows a geometric interpretation to be obtained which gives physical intuition to aid in designing a spacecraft rocket which will minimize or eliminate the deviation of the nutation angle.