MathLiveHamiltonian function (Legendre transform of the Lagrangian)
The Hamiltonian is obtained from the Lagrangian by a Legendre transform, summing each generalized momentum times its generalized velocity and subtracting the Lagrangian. It is the central function of Hamiltonian mechanics and often equals the total energy of the system.
H = \sum_i p_i \dot{q}_i - LWhat the symbols mean
| Hamiltonian function (energy-like quantity, in joules) | |
| generalized momentum conjugate to coordinate q_i | |
| generalized velocity, time derivative of coordinate q_i | |
| Lagrangian function (in joules) |
About this formula
- FieldPhysics
- TopicClassical mechanics
- LevelUniversity
- Also calledHamilton function, Hamiltonian from Lagrangian, Legendre transform Lagrangian to Hamiltonian, H equals sum p dot q minus L, Hamiltonian mechanics energy function, Hamiltonian definition
- SourceWikidata Q360356
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