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Symplectic connections and the linearisation of Hamiltonian systems

Marsden, J. E. and Ratiu, T. and Raugel, G. (1991) Symplectic connections and the linearisation of Hamiltonian systems. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 117 (3-4). pp. 329-380. ISSN 0308-2105. http://resolver.caltech.edu/CaltechAUTHORS:20100903-112241193

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Abstract

This paper uses symplectic connections to give a Hamiltonian structure to the first variation equation for a Hamiltonian system along a given dynamic solution. This structure generalises that at an equilibrium solution obtained by restricting the symplectic structure to that point and using the quadratic form associated with the second variation of the Hamiltonian (plus Casimir) as energy. This structure is different from the well-known and elementary tangent space construction. Our results are applied to systems with symmetry and to Lie-Poisson systems in particular.


Item Type:Article
Additional Information:© 1991. (Issued 17 April 1991). MS received 17 November 1989. Revised MS received 11 October 1990. Dedicated to Professor Jack K. Hale on the occasion of his 60th birthday. Partially supported by NSF grant DMS 8701318-01 and DOE Contract DE-AT03-88ER-12097. Partially supported by NSF grant DMS 8922699 and AFOSR/DARPA contract F49620-87-C-0118
Funders:
Funding AgencyGrant Number
NSFDMS 8701318-01
Department of EnergyDE-AT03-88ER-12097
NSFDMS 8922699
Air Force Office of Scientific Research (AFOSR)/Defense Advanced Research Projects Agency (DARPA)F49620-87-C-0118
Record Number:CaltechAUTHORS:20100903-112241193
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100903-112241193
Official Citation:Marsden, Jerrold E. ; Ratiu, Tudor S. ; Raugel, Geneviève In: Proceedings of the Royal Society of Edinburgh Sect. A, vol. 117, num. 3-4, 1991, p. 329-380
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19786
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:15 Sep 2010 18:42
Last Modified:26 Dec 2012 12:23

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