Solution of Kinematical Differential Equations for a Rigid Body

Abstract

This paper deals with the following problem: Given the orientation of a rigid body B at time t0 and the angular velocity of B for t ≥ t0 , find the orientation of B for t ≥ t0 . An approximate solution is found by employing an “averaging” technique and a lemma (proved in the paper) concerned with a special form of matrix exponentials. As a test, the heretofore unsolved problem of an axisymmetric rigid body subjected to the action of a body-fixed transverse torque of constant magnitude is worked out, and results are compared with those of a digital computer solution.