- #1
maverick280857
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Hello everyone.
I'm reading Goldstein's Classical Mechanics (2nd Ed) and I have worked out the derivation of Euler-Lagrange equation of motion from DAlembert's Principle as described in Chapter 1 and also the Action Integral approach in Chapter 2.
I want to understand the equivalence of the two approaches: the derivation from DAlembert's Principle works for forces of constraint that do no (virtual) work:
[tex]\sum_{i = 1}^{N}{\bf f_{i}\bullet \delta{\bf r_{i}} = 0[/tex]
But the derivation from the action principle does not make any explicit mention of the constraint forces. Since both eventually lead to the Euler-Lagrange condition [also refer to chapter 1 of http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/QM_Book.pdf] I think there should be some equivalence, but I can't see what it is.
Thanks..
I'm reading Goldstein's Classical Mechanics (2nd Ed) and I have worked out the derivation of Euler-Lagrange equation of motion from DAlembert's Principle as described in Chapter 1 and also the Action Integral approach in Chapter 2.
I want to understand the equivalence of the two approaches: the derivation from DAlembert's Principle works for forces of constraint that do no (virtual) work:
[tex]\sum_{i = 1}^{N}{\bf f_{i}\bullet \delta{\bf r_{i}} = 0[/tex]
But the derivation from the action principle does not make any explicit mention of the constraint forces. Since both eventually lead to the Euler-Lagrange condition [also refer to chapter 1 of http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/QM_Book.pdf] I think there should be some equivalence, but I can't see what it is.
Thanks..
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