Pages 34 and 35 of Whittaker's "A treatise on the analytical dynamics of particles and rigid bodies" ( http://books.google.com/books?id=OSckAAAAMAAJ&printsec=frontcover&dq=edmund+taylor+whittaker&cd=1#v=onepage&q=&f=false ) uses N's 2nd to eventually derive (and define) the kinetic energy. Then he goes on to show that a particular functional form on the kinetic energy holds (of course, these are the Euler-Lagrange equations), and eventually -- for conservative potentials -- that the Lagrangian is a useful concept.
I quite like this treatment, and he uses terms we probably wouldn't use today, such as (on page 55) "ignoration of coordinates", which are, of course, coordinates which don't have to enter into the problem because of constraint forces. That's a GREAT term for it.
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Down with categorical imperative!
flutzpah@yahoo.com
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