Solve Eqns with Lagrangean Action Integrals

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SUMMARY

The discussion centers on the application of Lagrangean mechanics and the derivation of Lagrange's equations, specifically focusing on the action integral S and its property of achieving a minimum value. Participants recommend studying the Calculus of Variation to understand these concepts better. A key resource mentioned is Mary Boas's "Mathematical Methods in the Physical Sciences," which provides accessible explanations suitable for undergraduate physics students. Additionally, Edwin Taylor's work on the least action principle is highlighted as a valuable reference.

PREREQUISITES
  • Understanding of Lagrangean mechanics
  • Familiarity with the action integral S
  • Basic knowledge of Calculus of Variation
  • Access to Mary Boas's "Mathematical Methods in the Physical Sciences"
NEXT STEPS
  • Study the Calculus of Variation in detail
  • Read Mary Boas's "Mathematical Methods in the Physical Sciences"
  • Explore Edwin Taylor's resources on the least action principle
  • Investigate the derivation of Lagrange's equations from first principles
USEFUL FOR

Students and educators in physics, particularly those studying classical mechanics and seeking to deepen their understanding of Lagrangean methods and the principles of least action.

nolanp2
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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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