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

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