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Spin Stability of Undamped Flexible Structures Rotating about the Minor Axis
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A method is presented for determining the nonlinear stability of undamped flexible structures spinning about the axis of minimum moment of inertia. Equations of motion are developed for structures that are free of applied forces and moments. The development makes use of a floating reference frame which follows the overall rigid body motion. Within this frame, elastic deformations are assumed to be given functions of n generalized coordinates. A transformation of variables is devised which shows the equivalence of the equations of motion to a Hamiltonian system with n + 1 degrees of freedom. Using this equivalence, stability criteria are developed based on the normal form of the Hamiltonian. It is shown that a motion which is spin stable in the linear approximation may be unstable when nonlinear terms are included. A stability analysis of a simple flexible structure is provided to demonstrate the application of the stability criteria. Results from numerical integration of the equations of motion are shown to be consistent with the predictions of the stability analysis.
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