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RESEARCH PAPERS

Solution of Kinematical Differential Equations for a Rigid Body

[+] Author and Article Information
T. R. Kane

Department of Applied Mechanics, Stanford University, Stanford, Calif.

J. Appl. Mech 40(1), 109-113 (Mar 01, 1973) (5 pages) doi:10.1115/1.3422907 History: Received July 01, 1971; Revised November 01, 1971; Online July 12, 2010

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.

Copyright © 1973 by ASME
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