Systemets [[dynamik]] er derfor beskrevet ved Euler-Lagrange-ligningen:
:<math> \frac{d}{dt}\left(\frac{\partial L}{\partial \dot x}\right)- \frac{\partial L}{\partial x} = 0</math>
:<math>\Downarrow</math>
:<math> \frac{d}{dt} \left(\frac{\partial \left(\frac{1}{2}m\dot x^2-V(x)\right)}{\partial \dot x}\right)- \frac{\partial \left(\frac{1}{2}m\dot x^2-V(x)\right)}{\partial x} = 0</math>
:<math>\Downarrow</math>
:<math> \frac{d}{dt} \left(m\dot x\right)+ \frac{\partial V(x)}{\partial x} = 0</math>
:<math>\Downarrow</math>
:<math> m\ddot x+ \frac{\partial V(x)}{\partial x} = 0</math>
:<math>\Downarrow</math>
{{NumBlk|:|<math>m\ddot x=-\frac{\partial V(x)}{\partial x}</math>|{{EquationRef|4}}}}
Videnskab Matematik