A set of dynamic equations governing the dynamics of a tethered satellite system and stabilizing tension control laws in feedback form are derived. The tether is assumed rigid and massless, and the equations of motion are derived using the system Lagrangian. It is observed that to stabilize the system, tools from stability analysis of critical nonlinear systems must be applied. Tools related to the Hopf bifurcation theorem are used in the construction of the stabilizing control laws, which may be taken as purely linear. Simulations illustrate the nature of the conclusions, and show that nonlinear terms in the feedback can be used to improve significantly the transient response.
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