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.
| Original language | English |
|---|---|
| Pages (from-to) | 1896-1903 |
| Number of pages | 8 |
| Journal | Journal of Mathematical Physics |
| Volume | 22 |
| Issue number | 9 |
| DOIs | |
| State | Published - 1981 |