Question

Derive Newton’ s second law in three dimension using the Lagrangian method.[6]

Answer 1

$$L=T-V\\\frac{\partial L}{\partial v}=mv\\\\\frac{\partial L}{\partial x}=-\frac{d U}{dx}\\m\frac{d v}{dt}=-\nabla V\\ma=F$$

so we again arrive at Newton’s second law, F = ma, now in three dimensions.