# American Institute of Mathematical Sciences

June  2011, 3(2): 261-275. doi: 10.3934/jgm.2011.3.261

## Euler-Poincaré reduction for systems with configuration space isotropy

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

Received  February 2010 Revised  June 2011 Published  July 2011

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.
Citation: Jeffrey K. Lawson, Tanya Schmah, Cristina Stoica. Euler-Poincaré reduction for systems with configuration space isotropy. Journal of Geometric Mechanics, 2011, 3 (2) : 261-275. doi: 10.3934/jgm.2011.3.261
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