Derive the Euler-Lagrange Equation (1/2)
Local covariant coordinates will be used in the following work.
- Start with a Lagrange density that is a function of the potential
and the derivative of the potential
(not position or velocity):
- Form the action:
- Take the variation of the action:
- Rewrite the 2nd term using the chain rule, subtracting the excess term:
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