Kinetic energy of an asymmetric rigid body moving around a fixed point: invariant representation in terms of quaternion matrices

The similarity transform and the properties of quaternion matrices are used to derive invariant expressions for the inertia matrix and kinetic energy of an asymmetric rigid body undergoing spatial motion around a fixed point in body-fixed and inertial frames of reference. The elements of the quaternion matrixes are Rodrigues–Hamilton parameters and quasi-velocities