Least Action via Computer

Bork, Alfred; Zellweger, Andres

doi:10.1119/1.1975584

Cited by 6 publications

(1 citation statement)

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“…Recently, the question whether the action for the classical world-line is a minimum or a saddle point and the fact that it is never a maximum have been addressed in detail [9]. However, even in the simplest case of a particle in one dimension, complete numerical [11,12] and graphical exploration of the global landscape of the action in the space of all world-lines is impossible. Therefore, although the Hamilton principle is oft stated [5] 2 as 'if you calculate the action for any world-line close to the classical world-line, it will be greater than the action for the classical world-line', this exercise is notably absent in all textbooks and is seldom explicitly carried out in the classroom.…”

Section: Introductionmentioning

confidence: 99%

Exploring the action landscape via trial world-lines

Joglekar¹,

Tham²

2010

Eur. J. Phys.

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The Hamilton action principle, also known as the principle of least action, and Lagrange equations are an integral part of intermediate and advanced undergraduate mechanics. Although the Hamilton principle is oft stated as "the action for any nearby trial world-line is greater than the action for the classical world-line", the landscape of action in the space of world-lines is rarely explored. Here, for three common problems from introductory physics -a free particle, a uniformly accelerating particle, and a simple harmonic oscillator -we present families of trial world-lines, characterized by a few parameters, that evolve continuously from their respective classical world-lines.With explicit analytical expressions available for the action, they permit a graphical visualization of the action landscape in the space of nearby world-lines. Although these trial world-lines form only a subset of the space of all nearby world-lines, they provide a pedagogical tool that complements the traditional Lagrange equation approach and is well-suited for advanced undergraduate students.

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Section: Introductionmentioning

confidence: 99%