Partial differential equations with differential constraints

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:220

Article

Krupková, O

关键词: fibered manifold;    dynamical form;    exterior differential system;    constraint submanifold;    non-holonomic constraint;    canonical distribution of a constraint;    constrained systems of PDEs;    constrained Lagrangian systems;   

DOI  :  10.1016/j.jde.2005.03.003

来源: Elsevier

【 摘 要 】

A geometric setting for constrained exterior differential systems on fibered manifolds with n-dimensional bases is proposed. Constraints given as submanifolds of jet bundles (locally defined by systems of first-order partial differential equations) are shown to carry a natural geometric structure, called the canonical distribution. Systems of second-order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds. As an important particular case, Lagrangian systems subjected to first-order differential constraints are considered. Different kinds of constraints are introduced and investigated (Lagrangian constraints, constraints adapted to the fibered structure, constraints arising from a (co)distribution, semi-holonornic constraints, holonomic constraints). (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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