The differential invariants of particle Lagrangians under equivalence by contact transformations (Q1915763)

The author studies the differential invariants of the integral \[ \int L(x,y^1,\dots,y^m,\dot y^1,\dots,\dot y^m)dx \] under the group of contact transformations on \(\mathbb{R}^{2m+1}\). This problem goes back to E. Cartan who gave the solution for \(m = 1\), and S. S. Chern, who solved the autonomous case for homogeneous Lagrangian functions. The results obtained in the present paper extend the ones previously obtained by R. Gardner and R. Bryant. The Cartan method of equivalence is widely used, and the results are interpreted in terms of Finsler geometry.