Natural dynamical connections
Alexandr Vondra (1991)
Czechoslovak Mathematical Journal
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Displaying similar documents to “A property of connections of mechanical systems of higher order”
Natural dynamical connections
Higher-order differential equations represented by connections on prolongations of a fibered manifold.
Alexandr Vondra (2000)
Extracta Mathematicae
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The main goal of the present work is a generalization of the ideas, constructions and results from the first and second-order situation, studied in [63], [64] to that of an arbitrary finite-order one. Moreover, the investigation extends the ideas of [65] from the one-dimensional base X corresponding to O.D.E.
Lifts of 1-forms to the tangent bundle of higher order
Jacek Gancarzewicz, Salima Mahi (1990)
Czechoslovak Mathematical Journal
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Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold.
Alexandr Vondra (1996)
Extracta Mathematicae
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Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
Jaime Muñoz Masqué (1985)
Revista Matemática Iberoamericana
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The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted...