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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/1995025