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Lobachevskii Journal of Mathematics, 2006, Volume 23, Pages 95–150 (Mi ljm19)  

Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems

O. Krupkováa, P. Volnýb

a Palacký University
b VŠB – Technical University of Ostrava
References:
Abstract: The paper is a survey of the theory of Lagrangian systems with non-holonomic constraints in jet bundles. The subject of the paper are systems of second-order ordinary and partial differential equations that arise as extremals of variational functionals in fibered manifolds. A geometric setting for Euler–Lagrange and Hamilton equations, based on the concept of Lepage class is presented. A constraint is modeled in the underlying fibered manifold as a fibered submanifold endowed with a distribution (the canonical distribution). A constrained system is defined by means of a Lepage class on the constraint submanifold. Constrained EulerЧ-Lagrange equations and constrained Hamilton equations, and properties of the corresponding exterior differential systems, such as regularity, canonical form, or existence of a constraint Legendre transformation, are presented. The case of mechanics (ODEТs) and field theory (PDEТs) are investigated separately, however, stress is put on a unified exposition, so that a direct comparison of results and formulas is at hand.
Keywords: jet bundles, non-holonomic constraints, semiholonomic constraints, holonomic constraints, constrained Lagrangian systems, constrained Euler–Lagrange equations, Hamilton–De Donder equations, regularity of constrained systems, momenta, Hamiltonian, Legendre transformation.
Submitted by: V. V. Lychagin
Received: 24.07.2006
Bibliographic databases:
Language: English
Citation: O. Krupková, P. Volný, “Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems”, Lobachevskii J. Math., 23 (2006), 95–150
Citation in format AMSBIB
\Bibitem{KruVol06}
\by O.~Krupkov\'a, P.~Voln\'y
\paper Differential equations with constraints in jet bundles: Lagrangian and Hamiltonian systems
\jour Lobachevskii J. Math.
\yr 2006
\vol 23
\pages 95--150
\mathnet{http://mi.mathnet.ru/ljm19}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2293367}
\zmath{https://zbmath.org/?q=an:1116.58002}
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