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Unformatted text preview: 2 F q i q j q i + 2 F tq j . (7) Because it is immaterial in which order partial di f erentiation is carried out, we can rewrite Eq.(7) as d dt F q j = q j " n X i =1 F q i q i + F t # = F q j , (8) 1 using Eq.(5) to replace the term in square brackets. From this result, we see that Eq.(4) is indeed satis f ed and that, therefore, Eq.(3) is also valid. Thus, Lagranges EOM are invariant under the operation of adding to the Lagrangian the total time derivative of a function F that depends only on the generalized coordinates and time. A more general result of this sort will be useful to us in Chapters 9 and 10. 2...
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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.
- Fall '10