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Euler–Poincaré Reduction on Principal Bundles

Abstract

Let π: PM be an arbitrary principal G-bundle. We give a full proof of the Euler–Poincaré reduction for a G-invariant Lagrangian L: J 1 P → R as well as the study of the second variation formula, the conservations laws, and study some of their properties.

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Castrillón López, M., García Pérez, P.L. & Ratiu, T.S. Euler–Poincaré Reduction on Principal Bundles. Letters in Mathematical Physics 58, 167–180 (2001). https://doi.org/10.1023/A:1013303320765

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  • calculus of variations
  • Euler–Poincaré equations
  • reconstruction
  • reduction
  • symmetries