Euler-Poincaré reduction  for systems with configuration space isotropy

Jeffrey K. Lawson; Tanya Schmah; Cristina Stoica

doi:10.3934/jgm.2011.3.261

Article Contents

2011, Volume 3, Issue 2: 261-275. Doi: 10.3934/jgm.2011.3.261

This issue Previous Article Sub-Riemannian and sub-Lorentzian geometry on $SU(1,1)$ and on its universal cover Next Article

Euler-Poincaré reduction for systems with configuration space isotropy

1.
Department of Mathematics and Computer Science, Western Carolina University, Cullowhee, NC 28723
2.
Department of Computer Science, University of Toronto, 10 King’s College Road, Room 3302, Toronto, ON, M5S 3G4
3.
Department of Mathematics, Wilfrid Laurier University, 75 University Ave West, Waterloo, ON, N2L 3C5

Received: January 31, 2010

Revised: May 31, 2011

Published: May 2011

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Abstract

This paper concerns Lagrangian systems with symmetries, near points with configuration space isotropy. Using twisted parametrisations corresponding to phase space slices based at zero points of tangent fibres, we deduce reduced equations of motion, which are a hybrid of the Euler-Poincaré and Euler-Lagrange equations. Further, we state a corresponding variational principle.

Keywords:

Symmetric Lagrangian,
slice theorem,
Euler-Poincaré reduction,
Euler-Poincaré-Lagrange bundle equations.

Mathematics Subject Classification: Primary: 70H03, 70H45.

Citation:

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