The Conversion of Rigid-Body Rotational Dynamics to Particle Dynamics

In this paper we present a new method that converts rigid-body rotational motion to particle translational motion in a high-dimensional space. The inertial terms in the equations of rigid-body rotational motion are nonlinear in nature, while those in the equations of particle motion are linear. Therefore, the problem of maneuvering the rotation of a rigid body can be handled more easily by the theory of equivalent particle dynamics than by the theory of rigid-body rotational dynamics. An example of a rigid body tracking the desired time-varying orientation by supplying it with an appropriate control torque is given.