MathLiveEuler-Lagrange equation
This equation states that a path extremizes the action integral of a Lagrangian L, so it gives the equations of motion in classical mechanics. It is the standard tool of the calculus of variations for finding functions that make a functional stationary.
\frac{\partial L}{\partial q}-\frac{d}{dt}\frac{\partial L}{\partial \dot{q}}=0What the symbols mean
| Lagrangian, kinetic energy minus potential energy (J) | |
| generalized coordinate | |
| time derivative of the generalized coordinate, generalized velocity | |
| time (s) |
About this formula
- FieldPhysics
- TopicClassical mechanics
- LevelUniversity
- Also calledLagrange equation, Euler-Lagrange equations of motion, principle of stationary action equation, calculus of variations equation, Lagrangian equation of motion, least action equation
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