Lagrange–Poincaré field equations

The Lagrange–Poincaré equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem....

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Bibliographic Details
Published in:Journal of geometry and physics 2011, Vol.61 (11), p.2120-2146
Main Authors: Ellis, David C.P., Gay-Balmaz, François, Holm, Darryl D., Ratiu, Tudor S.
Format: Article
Language:English
Subjects:
Conservation laws
Covariant reduction
Euler–Lagrange equations
Field theories
Mathematical Physics
Mathematics
Mechanics
Physics
Symmetries
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Summary:The Lagrange–Poincaré equations of classical mechanics are cast into a field theoretic context together with their associated constrained variational principle. An integrability/reconstruction condition is established that relates solutions of the original problem with those of the reduced problem. The Kelvin–Noether Theorem is formulated in this context. Applications to the isoperimetric problem, the Skyrme model for meson interaction, and molecular strands illustrate various aspects of the theory. ► The Lagrange–Poincaré equations of classical mechanics are cast into a field theoretic context. ► The associated constrained variational principle is derived. ► An integrability condition is established. ► The Kelvin–Noether Theorem is formulated in this context. ► Applications to the isoperimetric problem, the Skyrme model, and molecular strands illustrate the theory.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2011.06.007