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Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms

Marsden, J. E. and Wendlandt, J. M. (1997) Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms. In: Proceedings of the Symposium on Current and Future Directions in Mathematics. Birkhäuser , New York, NY, pp. 219-261. ISBN 081763956X.

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This paper studies variational principles for mechanical systems with symmetry and their applications to integration algorithms. We recall some general features of how to reduce variational principles in the presence of a symmetry group along with general features of integration algorithms for mechanical systems. Then we describe some integration algorithms based directly on variational principles using a discretization technique of Veselov. The general idea for these variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the original systems invariants, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. The resulting mechanical integrators are second-order accurate, implicit, symplectic-momentum algorithms. We apply these integrators to the rigid body and the double spherical pendulum to show that the techniques are competitive with existing integrators.

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Additional Information:© Springer Science+Business Media New York 1997. Research partially supported by DOE contract DE-FG03-95ER-25251 and the California Institute of Technology. Research partially supported by DOE contract DE-FG03-95ER-25251. / We thank Francisco Armero, Oscar Gonzalez, Abhi Jain, Ben Leimkuhler, Andrew Lewis, Robert MacKay, Richard Murray, George Patrick and Shmuel Weissman for useful discussions or comments.
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Department of Energy (DOE)DE-FG03-95-ER25251
Record Number:CaltechAUTHORS:20100910-132222147
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19872
Deposited By: Ruth Sustaita
Deposited On:16 Sep 2010 21:01
Last Modified:08 Nov 2021 23:55

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