Lagrange-Poincare field equations

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Ellis, David C. P.²  Gay-Balmaz, Francois^1,3  Holm, Darryl D.²  Ratiu, Tudor S.^4,5 

[1] CALTECH, Pasadena, CA 91125 USA

[2] Univ London Imperial Coll Sci Technol & Med, Dept Math, London SW7 2AZ, England

[3] Ecole Normale Super, CNRS, Lab Meteorol Dynam, Paris, France

[4] Ecole Polytech Fed Lausanne, Sect Math, CH-1015 Lausanne, Switzerland

[5] Ecole Polytech Fed Lausanne, Bernoulli Ctr, CH-1015 Lausanne, Switzerland

关键词: Field theories;    Symmetries;    Covariant reduction;    Euler-Lagrange equations;    Conservation laws;   

DOI  :  10.1016/j.geomphys.2011.06.007

来源: Elsevier

【 摘 要 】

The Lagrange-Poincare 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. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free