This project is concerned with the geometric study of so-called "Control Moment Gyroscopes" (CMGs), which are used for the controle of micro-satellites. Concepts from differential geometry, such as bundles and connections, are used to give a geometric interpretation of the dynamics of CMGs, with particular attention for the existence and analysis of singular states. Using this geometric formalism, a number of control-theoretic questions are being treated, such as the search for optimal trajectories between two given states.