Hernández-Garduño, Antonio and Marsden, J. E. (2005) Regularization of the Amended Potential and the Bifurcation of Relative Equilibria. Journal of Nonlinear Science, 15 (2). pp. 93-132. ISSN 0938-8974. doi:10.1007/s00332-004-0544-x. https://resolver.caltech.edu/CaltechAUTHORS:20100810-151931387
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Abstract
In the context of simple mechanical systems with symmetry, we give a method based on blowing up the amended potential for obtaining symmetry-breaking branches of relative equilibria bifurcating from a given set of symmetric relative equilibria. The general method is illustrated with two concrete mechanical examples, the double spherical pendulum and the symmetric coupled rigid bodies.
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| Additional Information: | © 2005 Springer Science+Business Media, Inc. Received October 3, 2002; accepted December 13, 2004. Online publication February 28, 2005. Communicated by J. Scheurle. We thank Petre Birtea, Juan-Pablo Ortega, George Patrick, Tudor Ratiu, Tanya Schmah, and Răzvan Tudoran for useful discussions and remarks concerning this paper. The first author gratefully acknowledges support from DGAPA-UNAM under project PAPIIT IN101902 and from CONACyT under project C01-42255-A, and the second author gratefully acknowledges support from the National Science Foundation. We thank the referees for their careful reading of the first version of this paper and for their suggestions that have led to numerous improvements. | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1007/s00332-004-0544-x | |||||||||
| Record Number: | CaltechAUTHORS:20100810-151931387 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20100810-151931387 | |||||||||
| Official Citation: | Hernández-Garduño, A., Marsden, J. Regularization of the Amended Potential and the Bifurcation of Relative Equilibria. J Nonlinear Sci 15, 93–132 (2005). https://doi.org/10.1007/s00332-004-0544-x | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 19379 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 13 Aug 2010 17:47 | |||||||||
| Last Modified: | 08 Nov 2021 23:51 |
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