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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
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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( …
20
votes
4
answers
11k
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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 …