UC San Diego

The Dzhanibekov and tennis racket phenomena are described by the torque-free rotation of a rigid body with three distinct principal moment of inertia values and angular velocity components. In these phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the intermediate principal moment of inertia, an unstable rotation is produced that leads to the basis of these phenomena. In this thesis, the above phenomena are examined and explained analytically, geometrically, and numerically. In addition, the analysis is applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. In the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Furthermore, the axisymmetric cases and the effect of varying intermediate principal moment of inertia are examined. Lastly, the analytical expressions are compared with the numerical simulation to validate the results. The complete solution is then summarized and shown to clearly demonstrate that the conservation of angular momentum is indeed preserved in the phenomena.