Stability of Liquid-Filled Spinning Spheroids Via Liapunov’s Second Method

[+] Author and Article Information
P. C. Parks

Department of Mathematics and Ballistics, Royal Military College of Science, Shrivenham, Swindon SN6 8LA, England

J. Appl. Mech 46(2), 259-262 (Jun 01, 1979) (4 pages) doi:10.1115/1.3424538 History: Received July 01, 1978; Revised September 01, 1978; Online July 12, 2010


In this paper the stability theory of Poincaré and others, expounded in the last few pages of Sir Horace Lamb’s textbook Hydrodynamics, is extended by a stability analysis using Liapunov functions to cover the full nonlinear equations of motion of spinning liquid-filled spheroids. The linearized criterion is confirmed, that is for stability c/a < 1 or c/a > 3 where the semiaxes of the spheroid are a, a, c, the c-axis being also the spin axis. The unstable motion for 1 < c/a < 3 is examined, and a conjecture that viscosity will destabilize spinning spheroids with c/a > 3 is proposed.

Copyright © 1979 by ASME
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