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arXiv · 2109.09094

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

David J. Tannor
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Abstract

A dual formalism for Lagrange multipliers is developed. The formalism is used to minimize an action function $S(q_2,q_1,T)$ 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.

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David J. Tannor. 2021-09-19. Duality of the Principle of Least Action: A New Formulation of Classical Mechanics. https://arxiv.org/abs/2109.09094

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