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]
Coisotropic variational problems
MUSSO, EMILIO;
2004
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
1-s2.0-S0393044003001670-main.pdf
accesso riservato
Tipologia:
2a Post-print versione editoriale / Version of Record
Licenza:
Non Pubblico - Accesso privato/ristretto
Dimensione
268.83 kB
Formato
Adobe PDF
|
268.83 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
https://hdl.handle.net/11583/1995025