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Any of several principles that find the physical trajectory of a system by minimizing or maximizing some value computed over the proposed path (for instance geometric optics can be reproduced by insisting on a minimum time principle).

2 votes
2 answers
2k views

Independent Variables of a Lagrangian [duplicate]

Let us consider a particle in one spatial dimension $x$ and one temporal dimension $t$. Its Lagrangian $L$ is given by \begin{eqnarray*} L &=& T- V \\ &=& \frac{1}{2} m\dot{x}^2 - V(x) \\ &=& L( …
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  • 3,053
20 votes
4 answers
11k views

How to derive source-free Maxwell's equations from the electromagnetic Lagrangian?

In Heaviside-Lorentz units the Maxwell's equations are: $$\nabla \cdot \vec{E} = \rho $$ $$ \nabla \times \vec{B} - \frac{\partial \vec{E}}{\partial t} = \vec{J}$$ $$ \nabla \times \vec{E} + \frac{\pa …
rainman's user avatar
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