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Homework Statement
I teach myself classical mechanics from David Tong
http://www.damtp.cam.ac.uk/user/tong/dynamics.html
From the homework set
I should verify that the Lagrangian
L=[itex]\frac{1}{12}m^{2}\dot{x}^{4}+m\dot{x}^{2}V-V^{2}[/itex]
Yields the same equations as the mere L=[itex]\frac{1}{2}m\dot{x}^{2}-V[/itex]
Homework Equations
Lagranges equation of motion
The Attempt at a Solution
This seems kinda trivial exercise, straightforward derivative computation yields
something like
[itex]m\dot{x}^{2}\left(\frac{\partial V}{\partial x}-m\ddot{x}\right)-2V\left(\frac{\partial V}{\partial x}+m\ddot{x}\right)=0[/itex]
which should somehow factor out and give simple equation.
Still, it does not seem to...
Could anyone help with this one?