Update 12.temporary_ins/44.relativity/30.n3/10.special-relativity/07.coherence/textbook.fr.md

12.temporary_ins/44.relativity/30.n3/10.special-relativity/07.coherence/textbook.fr.md

@@ -36,5 +36,52 @@ lessons:
 
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+Loi de transformation lorentzienne des positions :
+
+$`\left\{\begin{array}{l}
+ct' = \gamma\,(ct-\beta x)\\
+x'=\gamma\,(x - \beta c t)\\
+y'=y \\
+z=z 
+\end{array}\right.`$
+
+$`\overrightarrow{r}'=\overrightarrow{r}-\overrightarrow{V}\,t`$
+
+Loi de transformation lorentzienne des vitesses :
+
+en cours de rédaction, mà cest encore le cas galiéen :
+
+$`\left\{\begin{array}{l}
+dt' = dt \\
+\dfrac{dx'}{dt'}=\dfrac{dx}{dt}-V_x \\
+\dfrac{dy'}{dt'}=\dfrac{dy}{dt}-V_y \\
+\dfrac{dz'}{dt'}=\dfrac{dz}{dt}-V_z
+\end{array}\right.`$
+$`\quad\Longrightarrow\quad
+\left\{\begin{array}{l}
+\mathscr{v}_x'=\mathscr{v}_x-V_x \\
+\mathscr{v}_y'=\mathscr{v}_y-V_y \\
+\mathscr{v}_z'=\mathscr{v}_z-V_z
+\end{array}\right.`$
+
+$`\overrightarrow{\mathscr{v}}'=\overrightarrow{\mathscr{v}}-\overrightarrow{V}`$
+
+Loi de transformation galiléenne des accélérations :
+
+$`\left\{\begin{array}{l}
+dt' = dt \\
+\dfrac{d^2 x'}{dt'^2}=\dfrac{d}{dt}\big(\mathscr{v}_x-V_x\big)=\dfrac{d^2 x}{dt^2} \\
+\dfrac{d^2 y'}{dt'^2}=\dfrac{d}{dt}\big(\mathscr{v}_y-V_y\big)=\dfrac{d^2 y}{dt^2} \\
+\dfrac{d^2 z'}{dt'^2}=\dfrac{d}{dt}\big(\mathscr{v}_z-V_z\big)=\dfrac{d^2 z}{dt^2} \\
+\end{array}\right.`$
+$`\quad\Longrightarrow\quad
+\left\{\begin{array}{l}
+\mathscr{a}_x'=\mathscr{a}_x \\
+\mathscr{a}_y'=\mathscr{a}_y \\
+\mathscr{a}_z'=\mathscr{a}_z
+\end{array}\right.`$
+
+$`\overrightarrow{a}'=\overrightarrow{a}`$
+