Towards F=ma in a general setting for Lagrangian mechanics

Abstract

By using a suitably general definition of a force, one may geometrically cast the Euler-Lagrange equations in a ``force balance'' form. The key ingredient in such a construction is the Euler-Lagrange 2-force which is a bundle map from the bundle of two-jets into the first contact system. This 2-force can be used as the basis for a geometric presentation of Lagrangian mechanics with external forces and constraints. Also described is the precise correspondence between this 2-force and the Poincaré-Cartan two-form.