Commit a585b1e5 authored by Claude Meny's avatar Claude Meny

Update cheatsheet.fr.md

parent 0474a6c2
Pipeline #17914 canceled with stage
......@@ -265,18 +265,18 @@ par l'*angle $`\varphi`$* qui ainsi *varie entre $`0`$ et $`2\pi`$*.
**$`\displaystyle\mathbf{\overrightarrow{F}_{Laplace}}`$** *$`\displaystyle\mathbf{\,= \int_{\varphi=0}^{\varphi=\pi} \overrightarrow{dF}_{Laplace,\,P}}`$*
<br>
En **écriture matricielle** *dans le repère $`(O\,,\overrightarrow{e_x}\,,\overrightarrow{e_y}\,,\overrightarrow{e_z})`$* :
$`\displaystyle\mathbf{\large{\color{brown}{\overrightarrow{F}_{Laplace}}}}=I\,R\,\pmatrix{
<br>
$`\displaystyle\mathbf{\color{brown}{\overrightarrow{F}_{Laplace}}}=I\,R\,\pmatrix{
\int_0^{2\pi}\cos\,\varphi_P\,B_z\,d\varphi \\
\int_0^{2\pi}\sin\,\varphi_P\,B_z\,d\varphi \\
\int_0^{2\pi}(\sin\,\varphi_P\,B_y\;+\;\cos\,\varphi_P\,B_x)\,d\varphi}`$
$`\hspace{1cm}=I\,R\,\pmatrix{
\int_0^{2\pi}(\sin\,\varphi_P\,B_y+cos\,\varphi_P\,B_x)\,d\varphi}`$
<br>
$`=I\,R\,\pmatrix{
B_z\,\int_0^{2\pi}\cos\,\varphi_P\,d\varphi \\
B_z\,\int_0^{2\pi}\sin\,\varphi_P\,d\varphi \\
-B_y\,\int_0^{2\pi}\sin\,\varphi_P\,d\varphi\;-\;B_x\,\int_0^{2\pi}\cos\,\varphi_P\,d\varphi}`$
$`\hspace{1cm}=I\,R\,\pmatrix{0 \\0 \\0}=\mathbf{\large{\color{brown}{\overrightarrow{0}}}`$
-B_y\,\int_0^{2\pi}\sin\,\varphi_P\,d\varphi-B_x\,\int_0^{2\pi}\cos\,\varphi_P\,d\varphi}`$
<br>
$`=I\,R\,\pmatrix{0 \\0 \\0}=\mathbf{\color{brown}{\overrightarrow{0}}}`$
......
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