Simple derivation of Newtonian mechanics from the principle of least action

We present a method for introducing students to the classical principle of least action, using a novel approach based on the ordinary calculus of one variable. We define the classical action for a path and draw the connection between it and Newton’s laws for a free particle and for a particle in a c...

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Bibliographic Details
Published in:American journal of physics 2003-04, Vol.71 (4), p.386-391
Main Authors: Hanc, Jozef, Tuleja, Slavomir, Hancova, Martina
Format: Article
Language:English
Subjects:
Kinetics
Methods
Physics
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Summary:We present a method for introducing students to the classical principle of least action, using a novel approach based on the ordinary calculus of one variable. We define the classical action for a path and draw the connection between it and Newton’s laws for a free particle and for a particle in a conservative potential. The use of software to help students visualize the principle of least action and analyze rectilinear motion is discussed. We also briefly discuss the origin of the principle of least action in Feynman’s sum over paths formulation of quantum mechanics.
ISSN:0002-9505
1943-2909
DOI:10.1119/1.1528915