After deriving a set of dynamic equations governing the dynamics of a tethered satellite system (TSS), stabilizing tension-control laws are derived in feedback form. The tether is assumed to be 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 purely linear. Simulations illustrate the nature of the conclusions and show that nonlinear terms in the feedback can be used to significantly improve the transient response.
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