Title: Towards F=ma in a general setting for Lagrangian mechanics (33 pages)
Author(s): Andrew D. Lewis
Detail: Annales Henri Poincaré 1(3), pages 569-605, 2000
Journal version: Download

Original manuscript: 1998/05/19
Manuscript last revised: 1999/09/22

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.

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Last Updated: Fri Jul 10 07:05:20 2020

Andrew D. Lewis (andrew at mast.queensu.ca)