Commit b28d19cb authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent e6cadd25
Pipeline #13289 canceled with stage
......@@ -399,7 +399,7 @@ les composantes connues du vecteur $`\overrightarrow{dl}`$ :
Par définition :
$`\color{brown}{\large{\mathbf{d\phi=\overrightarrow{grad}\,\phi_M\cdot\overrightarrow{dl}}}}`$
$`\color{brown}{\mathbf{d\phi=\overrightarrow{grad}\,\phi_M\cdot\overrightarrow{dl}}}`$
$`\;=\big(X_{\alpha}\;\overrightarrow{e_{\alpha}}+X_{\beta}\;\overrightarrow{e_{\beta}}+X_{\gamma}\;\overrightarrow{e_{\gamma}}\big)
\cdot\big(dl_{\alpha}\;\overrightarrow{e_{\alpha}}+dl_{\beta}\;\overrightarrow{e_{\beta}}+dl_{\gamma}\;\overrightarrow{e_{\gamma}}\big)`$
......@@ -416,11 +416,11 @@ $`\begin{align}
+X_{\gamma}\,dl_{\gamma}\,\big(\overrightarrow{e_{\gamma}}\cdot\overrightarrow{e_{\gamma}}\big)\\
\end{align}`$
$`\color{brown}{\large{\mathbf{X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}}}}`$
$`\color{brown}{\mathbf{\quad = X_{\alpha}\,dl_{\alpha}+X_{\beta}\,dl_{\beta}+X_{\gamma}\,dl_{\gamma}}}`$
Par ailleurs,$`\phi`$ étant un champ scalaire, sa différentielle exprimée en coordonnées $`(\alpha\,,\beta\,,\gamma)`$ s'écrit :
$`\color{blue}{\large{\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}}}`$
$`\color{blue}{\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\alpha} + \left.\dfrac{\partial \phi}{\partial \beta}\right|_M\cdot dl_{\beta} + \left.\dfrac{\partial \phi}{\partial \gamma}\right|_M\cdot dl_{\gamma}}}`$
......
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