Duality of the Principle of Least Action: A New Formulation of Classical Mechanics

2021/09/19 by Tannor, David J.
#Classical Physics (physics.class-ph) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2109.09094

Abstract

A dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function S(q₂,q₁,T) without any dynamical input other than that S is convex. All the key equations of analytical mechanics -- the Hamilton-Jacobi equation, the generating functions for canonical transformations, Hamilton's equations of motion and S as the time integral of the Lagrangian -- emerge as simple consequences. It appears that to a large extent, analytical mechanics is simply a footnote to the most basic problem in the calculus of variations: that the shortest distance between two points is a straight line.

Related

• The Principle of Least Action as Interpreted by Nature and by the Observer
• Demystifying the Lagrangian of classical mechanics
• A Unifying Action Principle for Classical Mechanical Systems
• Two Hundred Years After Hamilton: The Simple Axiom That Underlies Classical Mechanics
• Back to Maupertuis' least action principle for dissipative systems: not\n all motions in Nature are most energy economical