Application of the Cayley Form to General Spacecraft Motion

The study of N-dimensional rigid-body motion is a well-developed field of mechanics. Some of the key results for describing the kinematics of these bodies come from the Cayley transform and the Cayley-transform kinematic relationship. Additionally, several forms of the equations of motion for these bodies have been developed by various derivations. By using Cayley kinematics, the motion of general mechanical systems can be intimately related to the motion of higher-dimensional rigid bodies. This is done by associating each point in the configuration space with an N-dimensional orientation. An example of this is the representation of general orbital and attitude motion of a spacecraft as pure rotation of a four-dimensional rigid body. Another example is the representation of a multibody satellite system as a four-dimensional rigid body.