PX285 - C3 - newton's second law

in newtonian mechanics:

L = T - V = \frac{1}{2} m v^{2} - V (x)

the first term of the euler-lagrange equation:

\frac{\partial L}{\partial x} = - \frac{\partial V}{\partial x} = F

where, $F$ , the force is given by the negative potential gradient

the second term:

- \frac{d}{d t} \frac{\partial L}{\partial v} = - \frac{d}{d t} (m v) = - \frac{d p}{d t}

where, $p$ is the momentum

therefore, the euler-lagrange equation gives:

F = \frac{d p}{d t}

the above relation is newton's second law
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