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Stability analysis of a rotating flexible system
Authors:Anthony M Bloch
Institution:(1) Mathematical Sciences Institute, Cornell University, 14853 Ithaca, NY, U.S.A.;(2) Department of Mathematics, Ohio State University, 43210 Columbus, OH, U.S.A.
Abstract:We analyse here the equations of motion of a planar body consisting of a rigid body with attached flexible rod. These equations take the form of coupled ordinary and partial differential equations. We analyse the equations both with and without centrifugal stiffening effects. Using the lsquoenergy-momentumrsquo method, we analyse nonlinear stability of the equilibria in each case. We also analyse the Hamiltonian and Poisson bracket structure of the system as well as the energy-momentum map and associated relative equilibria.Partly supported by NSF grant DMS-8701574 and AFOSR grant AFOSR-1SSA-87-0077 and by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.
Keywords:70F99  70K20  73C02  35P30
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