MathLiveHamilton–Jacobi equation
A first-order partial differential equation whose solution S, Hamilton's principal function, describes the motion of a classical system through its generalized coordinates and time. It is used to find trajectories in classical mechanics and to connect mechanics with wave optics and quantum theory.
-\frac{\partial S}{\partial t} = H\left(\boldsymbol{q}, \frac{\partial S}{\partial \boldsymbol{q}}, t\right)What the symbols mean
| Hamilton's principal function (action as a function of coordinates and time), in joule-seconds | |
| time, in seconds | |
| vector of generalized coordinates | |
| Hamiltonian function of the system, in joules |
About this formula
- FieldPhysics
- TopicClassical mechanics
- LevelAdvanced
- Also calledHJE, HJ equation, Hamilton Jacobi equation, principal function equation, classical mechanics partial differential equation, Hamilton principal function PDE
- SourceWikidata Q1060137
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