Abstract
Simple tests are developed to determine instability regions in the parameter space of flexible satellites. These tests are used in conjunction with Lyapunov's direct method to obtain exact stability boundaries in parameter space in cases where Lyapunov methods give only sufficient conditions for stability. In the case of Hamiltonian systems, the tests reduce to checking the sign of the determinant of the Hessian of the Hamiltonian at a single point. The Hamiltonian assumption can be relaxed to allow the inclusion of damping terms provided these terms have no linear dependence on position. Previous studies use complete or pervasive damping assumptions to obtain exact stability boundaries, whereas the proposed methods work for no damping or the damping described earlier. Examples illustrate the usefulness of the tests.
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