Solve Eqns with Lagrangean Action Integrals

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Lagrange's equations are derived from the principle of least action, which states that the action integral S takes a minimum value for the actual path taken by a system. To understand this concept, studying the Calculus of Variations is essential, as it provides the mathematical foundation for these principles. Recommended resources include Mary Boas's "Mathematical Methods in the Physical Sciences," which offers accessible explanations for undergraduates. Additionally, Edwin Taylor's work emphasizes the least action principle and provides further reading materials. Understanding these concepts is crucial for grasping the origins and applications of Lagrange's equations.
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i've been using langrangeans to solve eqns for a few months in class now but can't figure out where lagrange's equations actually come from. my problem is that i can't understand why the action integral S always takes a minimum value. can anyone help me with this?
 
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nolanp2 said:
i've been using langrangeans to solve eqns for a few months in class now but can't figure out where lagrange's equations actually come from. my problem is that i can't understand why the action integral S always takes a minimum value. can anyone help me with this?

What you want to study is what is known as the Calculus of Variation. This is often found in mathematical physics text/courses. The best source to start is Mary Boas's text "Mathematical Methods in the Physical Sciences", a book that I recommend all physics undergraduate to get. She has a whole chapter on the calculus of variation that is very easy to follow at the undergraduate level.

Other than that, you may want to get a few sources from Edwin Taylor's page, who is a strong advocate on the teaching of the least action principle ahead of the standard Newtonian "force" concept. He has several links to his papers here:

http://www.eftaylor.com/leastaction.html

Zz.
 

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