The fundamental form of a second-order homogeneous Lagrangian in two variables

D. J. Saunders

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arXiv · math/0512384

The fundamental form of a second-order homogeneous Lagrangian in two variables

D. J. Saunders

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Abstract

We construct, for a second-order homogeneous Lagrangian in two independent variables, a differential 2-form with the property that it is closed precisely when the Lagrangian is null. This is similar to the property of the 'fundamental Lepage equivalent' associated with first-order Lagrangians defined on jets of sections of a fibred manifold. We show that this form may be defined on a fourth-order frame bundle but is not, in general, projectable to a bundle of contact elements

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D. J. Saunders. 2005-12-16. The fundamental form of a second-order homogeneous Lagrangian in two variables. https://arxiv.org/abs/math/0512384

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