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Published 2008 | Accepted Version
Book Section - Chapter Open

Relaxed matching for stabilization of relative equilibria of mechanical systems

Abstract

The method of controlled Lagrangians is a technique for stabilizing relative equilibria of mechanical systems with symmetry. This paper develops a modication 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.

Additional Information

DAL and DVZ were partially supported by NSF grants DMS-0306017 and DMS- 0604108. AMB was supported in parts by NSF grants CMS-0408542 and DMS- 604307. JEM was partially supported by AFOSR grant FA9550-08-1-0173.

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August 19, 2023
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October 20, 2023