THE GEOMETRY OF TIME-DEPENDENT LAGRANGIANS

A generalization of Lagrange geometry appropriate for time-dependent Lagrangians arising in physics and biology, called rheonomic Lagrange geometry, is developed. Nonlinear and linear connections, their torsions, curvatures and deflections are explicitly given. Almost contact structures in rheonomic Lagrange spaces are characterized. Maxwell's equations, for a given Lagrangian determined deflection tensor, are derived.