Equations · equation
Euler–Lagrange Equation
Classical Field Theory · 1788
- Equation
- d/dt (∂L/∂q̇) − ∂L/∂q = 0
- Field
- Classical Field Theory
- Named After
- Leonhard Euler · Joseph-Louis Lagrange
- Year
- 1788
Symbols
L the Lagrangian · q a generalized coordinate (any convenient variable) · q̇ its rate of change · one equation per coordinate, whatever the coordinates
Significance
Least action turned into a machine: write down L, turn the crank, out come the equations of motion — in any coordinates, no forces to draw. Newton's F = ma falls out as a special case; so do pendulums on carts, orbits, and (with L a field density) Maxwell and Einstein.
Referenced by
equation
theory
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