Equations de d'Alembert

Un article de wiki sillages.info.

\newcommand{\rot}{\overrightarrow{\mathrm{rot}}} \newcommand{\diff}[2]{\frac{\partial #1}{\partial #2}} \newcommand{\grad}{\overrightarrow{\mathrm{grad}}} \renewcommand{\div}{\mathrm{div}}


\mathrm{div} \vec{E} =\frac{\rho}{\epsilon_0} \overrightarrow{\mathrm{rot}} \vec E = -\frac{\partial \vec B}{\partial t} \rot \vec B = \mu_0 \vec{\jmath} + \frac{1}{c^2} \diff{\vec E}{t} \frac{d}{dt}\left[\iiint_{V} \Big(\frac{1}{2}\varepsilon_0 \vec{E}^2 + \frac{1}{2} \frac{\vec B^2}{\mu_0} \Big) d\tau\right] =
	- \iint_{S} \frac{\vec E\wedge \vec B}{\mu_0} . \vec n \,d S - \iiint_{V}\vec\jmath . \vec E \,d \tau

\begin{cases}
	  \ddot{x}_1  = -\Omega_1^2 x_1 - \Omega_2^2 x_2\\
	  \ddot{x}_2 = -\Omega_2^2 x_1 - \Omega_1^2 x_1
	\end{cases}

\begin{array}{|l|c|r|l|} \hline
	354 & 3541 & 1354131 & 3541 \\ \hline
	12  & 12   & 2113    & 354 \\ \hline
	\end{array}

</math>\vec \Delta = \grad \, \div - \rot \, \rot </math>

--OlivierGranier 9 janvier 2014 à 12:16 (CET)