The geometry of ordinary variational equations / Olga Krupková
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1678Langue : anglais.Éditeur : Berlin : Springer, 1997ISBN: 9783540638322.ISSN: 1617-9692.Sujet MSC : 70H50, Mechanics of particles and systems, Higher-order theories for problems in Hamiltonian and Lagrangian mechanics49K15, Calculus of variations and optimal control; optimization, Optimality conditions for problems involving ordinary differential equations
58E30, Global analysis, analysis on manifolds, Variational principles in infinite-dimensional spaces
70H03, Mechanics of particles and systems, Hamiltonian and Lagrangian mechanics - Lagrange's equations
70H20, Mechanics of particles and systems, Hamilton-Jacobi equations in mechanicsEn-ligne : Springerlink | Zentralblatt | MathSciNet
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This book, which is an enlarged version of the author's Ph.D. thesis, gives a comprehensive and self-contained geometrical treatment of systems of ordinary variational differential equations (i.e. Euler-Lagrange equations) of any finite order. The general geometric framework is that of jet prolongations of a fibred manifold over a 1-dimensional base space. A notion which plays a central role in the approach advocated by the author, is that of Lepagean forms. ... (MathSciNet)
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