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With that convention, and with the assumption that we're working in an inertial frame with Cartesian coordinates, let's write out the kinetic energy and some of its derivatives (watch out for those "flyspec" dots over the q's -- they almost shrank out of existence when LaTex typeset the equations!): For an ordinary potential function, which doesn't depend on velocity, we can also write: (Note that we wrote "Fi" for the ith component of the force vector there, which is a little different from what we were using subscripts for back in (1a).) Now, plugging the derivatives in (5) and (6) into equation (4) for the Lagrangian, we see that: And so, for Cartesian coordinates, using equation ( 4 ) for our Lagrangian, equation ( 3 ) is equivalent to Newton's second law.

Pages: 248

Publisher: Springer; Softcover reprint of the original 1st ed. 2003 edition (December 21, 2012)

ISBN: 1461265525

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