I am watching Susskind's derivation of Newton's F=ma from the Euler-Lagrange equations (53 minutes in) here http://www.youtube.com/watch?v=3apIZCpmdls for which he uses the Lagrangian of kinetic energy minus potential energy. I have seen this done elsewhere as well. As far as I can tell, and please correct me if I'm wrong, the only reason to do this is because by convention we define F as the negative of the derivative of potential so subtracting potential energy in the Lagrangian will lead directly to F=ma and not -F=ma. I guess my real question is, is there any reason why we can't just change the convention of having F be equal to the negative derivative of potential energy so we would be able to write the Lagrangian as kinetic plus potential energy (as it feels like it should be)?
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