(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

Lagranges equation of motion

3. 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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lagrangian -> Equation of motion derivation

**Physics Forums | Science Articles, Homework Help, Discussion**