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. http://resolver.caltech.edu/CaltechAUTHORS:20101006-100038652
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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.
|Item Type:||Book Section|
|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.|
|Subject Keywords:||Controlled Lagrangians, kinetic shaping|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||19 Nov 2010 19:09|
|Last Modified:||26 Dec 2012 12:30|
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