Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500507 | Differential Geometry and its Applications | 2005 | 16 Pages |
Abstract
We consider multiple-integral variational problems where the Lagrangian function, defined on a frame bundle, is homogeneous. We construct, on the corresponding sphere bundle, a canonical Lagrangian form with the property that it is closed exactly when the Lagrangian is null. We also provide a straightforward characterization of null Lagrangians as sums of determinants of total derivatives. We describe the correspondence between Lagrangians on frame bundles and those on jet bundles: under this correspondence, the canonical Lagrangian form becomes the fundamental Lepage equivalent. We also use this correspondence to show that, for a single-determinant null Lagrangian, the fundamental Lepage equivalent and the Carathéodory form are identical.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Crampin, D.J. Saunders,