Parameter-invariant second-order variational problems in one variable



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Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel (1998) Parameter-invariant second-order variational problems in one variable. Journal of physics A: Mathematical and general, 31 (29). pp. 6225-6242. ISSN 0305-4470

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A projection is defined such that a second-order Lagrangian density factors through this projection module contact forms if and only if it is parameter invariant. In this way, a geometric interpretation of the parameter invariance conditions is obtained. The above projection is then used to prove the strict factorization of the Poincare-Cartan form attached to a parameter-invariant variational problem thus leading us to state the Hamilton-Cartan formalism, the complete description of symmetries and regularity for such problems. The case of the squared curvature Lagrangian in the plane is analysed especially.

Item Type:Article
Uncontrolled Keywords:Second-order Lagrangian density; Parameter invariance; Poincare-Cartan form; Squared curvature Lagrangian
Subjects:Sciences > Mathematics > Differential geometry
ID Code:17496
Deposited On:20 Dec 2012 10:55
Last Modified:12 Dec 2018 15:13

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