The motion behaviors of a rigid body can be characterized by a six degrees of freedom motion trajectory, which contains the 3-D position vectors of a reference point on the rigid body and 3-D rotations of this rigid body over time. This paper devises a rotation and relative velocity (RRV) descriptor by exploring the local translational and rotational invariants of rigid body motion trajectories, which is insensitive to noise, invariant to rigid transformation and scale. The RRV descriptor is then applied to characterize motions of a human body skeleton modeled as articulated interconnections of multiple rigid bodies. To show the descriptive ability of our RRV descriptor, we explore its potentials and applications in different rigid body motion recognition tasks. The experimental results on benchmark datasets demonstrate that our RRV descriptor learning discriminative motion patterns can achieve superior results for various recognition tasks.