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ANALYTICAL METHODS FOR DETERMINING EXACT STABILITY BOUNDARIES FOR FLEXIBLE STRUCTURES

Simple tests are developed to determine instability regions for general classes of systems in parameter space. Simplifications of the tests for even dimensional, Hamiltonian, second order, and damped syst e m are derived. These tests are used in conjunction with Liapunov’s direct method to obtain exact stability boundaries in parameter space in cases where Liapunov methods give only sufficient conditions for stability. An example of a flexible rotor system is given illustrating the usefulness of the tests.