## anonymous 4 years ago Is the definition \-[\frac{\partial \mathbf{U}}{\partial \mathbf{x}}=\mathbf{F}\] arrived at only by minimising action (that is, using the Euler-Lagrange equation) and F=ma (that is, is there any other equally thorough way of doing it)?

1. anonymous

That is, if you assume $T=0.5mv^2$ and $U=U$, and plug this into the Euler-Lagrange equation, you get $m\ddot{x}=\frac{dU}{dx}$. Is this the only fundamental way to get to this equation, or is it only one example of many equally fundamental ones?

2. anonymous

*with a minus sign, of course