On the inverse problem of the calculus of variations
- 1 September 1981
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 22 (9) , 1896-1903
- https://doi.org/10.1063/1.525162
Abstract
We consider the inverse problem of the calculus of variations for any system by writing its differential equations of motion in first-order form. We provide a way of constructing infinitely many Lagrangians for such a system in terms of its constants of motion using a covariant geometrical approach. We present examples of first-order Lagrangians for systems for which no second-order Lagrangians exist. The Hamiltonian theory for first-order (degenerate) Lagrangians is constructed using Dirac’s method for singular Lagrangians.Keywords
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