Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

[+] Author and Article Information
L. A. Month

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, Calif. 94720

R. H. Rand

Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, N.Y. 14853

J. Appl. Mech 52(3), 686-692 (Sep 01, 1985) (7 pages) doi:10.1115/1.3169122 History: Received August 01, 1984; Revised October 01, 1984; Online July 21, 2009


This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

Copyright © 1985 by ASME
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