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Relaxed matching for stabilization of relative equilibria of mechanical systems

Long, D. A. and Bloch, A. M. and Marsden, J. E. and Zenkov, D. V. (2008) Relaxed matching for stabilization of relative equilibria of mechanical systems. In: Proceedings of the 18th International Symposium on Mathematical Theory of Networks and Systems. , Blacksburg, VA, pp. 1-12.

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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.

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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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Air Force Office of Scientific Research (AFOSR) FA9550-08-1-0173
Subject Keywords:Controlled Lagrangians, kinetic shaping
Record Number:CaltechAUTHORS:20101006-100038652
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20320
Deposited By: Tony Diaz
Deposited On:19 Nov 2010 19:09
Last Modified:26 Dec 2012 12:30

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