Euler-Lagrange equation

Equivalent to the Principle of Least Action.

Equation

Form like $L(q,\dot{q},t)$, it has the equation:

$$\frac{d}{dt}(\frac{\partial L}{\partial \dot{q}})=\frac{\partial L}{\partial q}$$

It is equivalent to Principle of Least Action.

Remarks

For this equation, when L and L’ only has a time differentiate difference: $\frac{\partial F}{\partial t}$, it will not has anything special in the equation.

Related

• Calculus of Variations
• Brachistochrone problem
• Noether’s theorem