In this paper we study constrained variationalproblems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then the extremal curves can be found by quadratures. Our proof is constructive and relies on the reduction theory for coisotropic optimal control problems. This gives a unified explanation of the integrability of several classical variationalproblems such as the total squared curvature functional, the projective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincaré variationalproblems.
Coisotropic variational problems / Musso, Emilio; J. D. E., Grant. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - STAMPA. - 50:(2004), pp. 303-338. [10.1016/j.geomphys.2003.10.005]
Titolo: | Coisotropic variational problems | |
Autori: | ||
Data di pubblicazione: | 2004 | |
Rivista: | ||
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.geomphys.2003.10.005 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
---|---|---|---|---|
1-s2.0-S0393044003001670-main.pdf | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/1995025