## Rigid Bodies

Each rigid body has three translational degrees of freedom (DOF) and rotational DOF (Euler parameter), which describe the orientation of the body. The origin of the body coordinate system is located at the center of mass. This decouples the translational movement of the body from the rotational. Moreover, the orientation of the body coordinate system is such that the axes of the body coordinate system are along the principle axes of inertia of the body.

The location of the center of mass represents the initial translational degrees of freedom, while the rotation matrix defines the initial values of the four Euler parameters.