[PDF] Stability and long-time behaviour of a rigid body containing a damper-论文阅读讨论-ReadPaper

摘要

This paper provides a comprehensive analysis of stability and long-timebehaviour of a coupled system constituted by two rigid bodies separated by athin layer of lubricant. We show that permanent rotations of the whole system,with the solids at relative rest, are exponentially stable if and only if theaxis of rotation is the principal axis of inertia corresponding to the largestmoment of inertia of the outer body. All other equilibria are normallyhyperbolic, and hence unstable. In addition, we show that all solutions to thegoverning equations converge to an equilibrium configuration, no matter theinitial conditions are chosen. Numerical evidence of the above results as wellas conditions ensuring attainability of the stable configurations are alsopresented. For the stability analysis we use a linearization principle for dynamicalsystems possessing a center manifold. The characterization of the long-timebehaviour is obtained by a careful analysis of the partially dissipative systemof equations governing the motion of the coupled system.

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