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The Stability Conditions for a Heavy Solid Motion

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  • A. I. Ismail

Abstract

In this paper, the stability conditions for the rotary motion of a heavy solid about its fixed point are considered. The center of mass of the body is assumed to lie on the moving z -axis which is assumed to be the minor axis of the ellipsoid of inertia. The nonlinear equations of motion and their three first integrals are obtained when the principal moments of inertia are distributed as . We construct a Lyapunov function L to investigate the stability conditions for this motion. We give a numerical example to illustrate the necessary and sufficient conditions for the stability of the body at certain moments of inertia. This problem has many important applications in different sciences.

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  • A. I. Ismail, 2020. "The Stability Conditions for a Heavy Solid Motion," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-4, October.
    • Handle: RePEc:hin:jnlmpe:8829439
    DOI: 10.1155/2020/8829439
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