The action principle

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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 cant understand why the action integral S always takes a minimum value. can anyone help me with this?
 

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ZapperZ
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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 cant 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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