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June 2010 Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids
Ari Stern
J. Symplectic Geom. 8(2): 225-238 (June 2010).

Abstract

We present a discrete analog of the recently introduced Hamilton– Pontryagin variational principle in Lagrangian mechanics. This unifies two, previously disparate approaches to discrete Lagrangian mechanics: either using the discrete Lagrangian to define a finite version of Hamilton’s action principle, or treating it as a symplectic generating function. This is demonstrated for a discrete Lagrangian defined on an arbitrary Lie groupoid; the often encountered special case of the pair groupoid (or Cartesian square) is also given as a worked example.

Citation

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Ari Stern. "Discrete Hamilton-Pontryagin mechanics and generating functions on Lie groupoids." J. Symplectic Geom. 8 (2) 225 - 238, June 2010.

Information

Published: June 2010
First available in Project Euclid: 15 July 2010

zbMATH: 1375.70057
MathSciNet: MR2670166

Rights: Copyright © 2010 International Press of Boston

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Vol.8 • No. 2 • June 2010
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