On null Lagrangians

Year, pages: 2015, 1063 - 1078

We consider Lagrangians for parametric variational problems defined on velocity manifolds and show that a Lagrangian is null precisely when its shadow, a family of vector forms, is closed. We also show that a null Lagrangian can be recovered (to within a constant) from its shadow, and therefore that such a Lagrangian is (again to within a constant) a sum of determinants of total derivatives.

Saunders, D. 2015. On null Lagrangians. In Mathematica Slovaca, vol. 65, no.5, pp. 1063-1078. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0073

Saunders, D. (2015). On null Lagrangians. Mathematica Slovaca, 65(5), 1063-1078. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0073