Global Lagrangian and Hamiltonian formalisms for higher order calculus of variations over fibered manifolds are investigated, The role uf so-called "fibered connections"is pointed out, especially in view of the properties related tn the existence of a global Poincaré-Cartan form. A strong regularity condition on the Lagrangian allows to define a bundle isomorphism, which generalizes the classical Legendre transformation, and to discuss the notion of Hamiltoniall extremals in the hyperregular case.
Global formalisms in higher order calculus of variations
FERRARIS, Marco;FRANCAVIGLIA, Mauro
1984-01-01
Abstract
Global Lagrangian and Hamiltonian formalisms for higher order calculus of variations over fibered manifolds are investigated, The role uf so-called "fibered connections"is pointed out, especially in view of the properties related tn the existence of a global Poincaré-Cartan form. A strong regularity condition on the Lagrangian allows to define a bundle isomorphism, which generalizes the classical Legendre transformation, and to discuss the notion of Hamiltoniall extremals in the hyperregular case.
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