Commit b26df1e7 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 19d5adc0
Pipeline #13300 canceled with stage
...@@ -433,16 +433,17 @@ $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\ ...@@ -433,16 +433,17 @@ $`\mathbf{d\phi=\left.\dfrac{\partial \phi}{\partial \alpha}\right|_M\cdot dl_{\
La comparaison terme à terme de ces deux expressions de $'d\phi`$ donne : La comparaison terme à terme de ces deux expressions de $'d\phi`$ donne :
$`X_{\alpha}=\dfrac{\partial \phi}{\partial \alpha}\,\dfrac{\partial \alpha}{\partial dl_{\alpha}}`$ $`X_{\alpha}=\dfrac{\partial \phi}{\partial \alpha}\,\dfrac{\partial \alpha}{\partial dl_{\alpha}}`$ ,
$`X_{\beta}=\dfrac{\partial \phi}{\partial \beta}\,\dfrac{\partial \beta}{\partial dl_{\beta}}`$ $`X_{\beta}=\dfrac{\partial \phi}{\partial \beta}\,\dfrac{\partial \beta}{\partial dl_{\beta}}`$ ,
$`X_{\alpha}=\dfrac{\partial \phi}{\partial \gamma}\,\dfrac{\partial \gamma}{\partial dl_{\gamma}}`$ $`X_{\alpha}=\dfrac{\partial \phi}{\partial \gamma}\,\dfrac{\partial \gamma}{\partial dl_{\gamma}}`$
Soit Soit
$`\color{brown}{\mathbf{\overrightarrow{grad}\,\phi= $`\color{brown}{\mathbf{
\dfrac{\partial \alpha}{\partial dl_{\alpha}\,\dfrac{\partial \phi}{\partial \alpha}\,\overrightarrow{e_{\alpha}} \overrightarrow{grad}\,\phi=
+\dfrac{\partial \beta}{\partial dl_{\beta}\,\dfrac{\partial \phi}{\partial \beta\,\overrightarrow{e_{\beta}} \dfrac{\partial \alpha}{\partial dl_{\alpha}}\,\dfrac{\partial \phi}{\partial \alpha}\,\overrightarrow{e_{\alpha}}
+\dfrac{\partial \gamma}{\partial dl_{\gamma}\,\dfrac{\partial \phi}{\partial \gamma}\,\overrightarrow{e_{\gamma}} +\dfrac{\partial \beta}{\partial dl_{\beta}}\,\dfrac{\partial \phi}{\partial \beta}\,\overrightarrow{e_{\beta}}
+\dfrac{\partial \gamma}{\partial dl_{\gamma}}\,\dfrac{\partial \phi}{\partial \gamma}\,\overrightarrow{e_{\gamma}}
}}`$ }}`$
......
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