Abstract
Abstract 10.1. In each case the origin is an equilibrium point of the autonomous system. where A, B and C (all different) are the principal moments of inertia, and (ω1, ω2, ω3) is the spin of the body in principal axes fixed in the body. Find all the states of steady spin of the body. is a Liapunov function for the case when A is the largest moment of inertia, so that this state is stable. Suggest a Liapunov function which will establish the stability of the case in which A is the smallest moment of inertia. Are these states asymptotically stable? Why would you expect V as given above to be a first integral of the Euler equations? Show that each of the terms in braces is such an integral Since ˙ V =0, then the level curves of V coincide with the solutions of the Euler equations. One conclusion is that the equilibrium states are not asymptotically stable. The second conclusion is that V must be composed of first integrals of the Euler equations in some manner.
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