Variational principles for locally variational forms
- Department of Mathematics, Presov University, 08001 Presov (Slovakia)
We present the theory of higher order local variational principles in fibered manifolds, in which the fundamental global concept is a locally variational dynamical form. Any two Lepage forms, defining a local variational principle for this form, differ on intersection of their domains, by a variationally trivial form. In this sense, but in a different geometric setting, the local variational principles satisfy analogous properties as the variational functionals of the Chern-Simons type. The resulting theory of extremals and symmetries extends the first order theories of the Lagrange-Souriau form, presented by Grigore and Popp, and closed equivalents of the first order Euler-Lagrange forms of Hakova and Krupkova. Conceptually, our approach differs from Prieto, who uses the Poincare-Cartan forms, which do not have higher order global analogues.
- OSTI ID:
- 20699178
- Journal Information:
- Journal of Mathematical Physics, Vol. 46, Issue 5; Other Information: DOI: 10.1063/1.1901323; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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