Covariant inverse problem of the calculus of variations
- 1 July 1977
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 18 (7) , 1367-1373
- https://doi.org/10.1063/1.523430
Abstract
The solution of the covariant inverse problem of the calculus of variations (that of finding a Lagrangian for a given set of dynamical equations) is presented as a generalization flat space formalism of Atherton and Homsy. Known Lagrangians such as those for the complkex scalar field, vector gauge fields, and Einstein’s equations are used as examples. Additional insight into the formalism is provided by new examples that include a two-tensor theory, a method for obtaining conservation laws directly from dynamical equations, and a Hamiltonian formulation for higher order, nonlinear, differential equations.Keywords
This publication has 3 references indexed in Scilit:
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- On the Existence and Formulation of Variational Principles for Nonlinear Differential EquationsStudies in Applied Mathematics, 1975
- -Dominance of GravityPhysical Review D, 1971