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Relaxed Matching for Stabilization of Mechanical Systems

The method of controlled Lagrangians is a technique for stabilizing relative equilibria of mechanical systems with symmetry. This paper develops a modification of kinetic shaping technique in the theory of controlled Lagrangians. The main idea is that the dynamics associated with the controlled Lagrangian is amended by non-conservative forces that act in the shape directions; this gives additional freedom and hence applicability to the method. The usefulness of this methodology is demonstrated on the pendulum on a rotor arm.