The intent of this project is to develop a general analytic theory of the dynamical motion of axisymmetric rigid bodies subject to arbitrary body fixed forces and moments. The problem has received some attention in the past by classical dynamicists and more recently, in a restricted form, by Bodewadt. Unfortunately,the general problem has not been solved and may be unsolvable by current methods. Furthermore, the Bodewadt solution may be in error. The research focuses on four topics including the Euler equations of motion, the Eulerian angles, controlling the angular momentum vector, and the translational acceleration equations. Each of these is further subdivided into sub topics. For the first, attention is directed toward finding an analytical solution when the transverse angular rates are not small, and toward the case of time varying body fixed torques. The Eulerian angles analysis attempts to simplify existing solutions, and to adjust the solutions to account for time varying body fixed torques. The angular momentum study derives solutions for the angular momentum based on solutions for the Eulerian angles. Lastly, the acceleration equations study focuses on deriving expressions for velocity and position of the rigid body. This research enhances the general knowledge base in analytical dynamics. It has applications in the knowledge and control of spinning and thrusting bodies such as spacecraft and rockets.
