Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold.

Alexandr Vondra

Displaying similar documents to “Prolongations and fields of paths for higher-order O.D.E. represented by connections on a fibered manifold.”

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.

Natural dynamical connections

Alexandr Vondra (1991)

Czechoslovak Mathematical Journal

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A property of connections of mechanical systems of higher order

Anton Dekrét (1993)

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Hamilton extremals in higher order mechanics

Demeter Krupka, Jana Musilová (1984)

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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...

Multivector fields and connections. Applications to field theories.

Arturo Echeverría-Enríquez, Miguel Carlos Muñoz-Lecanda, Narciso Román-Roy (2002)

RACSAM

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Se estudia la integrabilidad de campos multivectoriales en variedades diferenciables y la relación entre algunos tipos de campos multivectoriales en un fibrado de jets y conexiones en dicho fibrado. Como caso particular se relacionan los campos multivectoriales integrables y las conexiones cuyas secciones integrales son holonómicas. Como aplicación de todo ello, estos resultados permiten escribir las ecuaciones de campo de las teorías clásicas de campos de primer orden en varias formas...