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Commit 0ec8d33f authored by Claude Meny's avatar Claude Meny
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Update cheatsheet.fr.md

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    12.temporary_ins/08.conservative-vector-fields/20.conservative-vector-fields-properties/20.overview/cheatsheet.fr.md
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    ...@@ -529,37 +529,20 @@ x* La **circulation de la force conservative** s'exerçant sur un corpuscule de ...@@ -529,37 +529,20 @@ x* La **circulation de la force conservative** s'exerçant sur un corpuscule de
    $`\begin{align} $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\ \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\ & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\
    $ =-\,\int_A^B \alpha\,d\phi_X \\
    $ =-\,\int_A^B \mathcal{E}_X^{pot} \\
    \\
    & \color{brown}{\large{\mathbf{\;=-\,\mathcal{E}_X^{pot}(B)-\mathcal{E}_X^{pot}(A)}}}\\
    \\
    & \color{blue}{\large{\mathbf{\;=\overset{B}{\underset{A}{\Large{\Delta}}}(\mathcal{E}_X^{pot})}}}\\
    \end{align}`$
    <br>
    <br>
    $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    \end{align}`$
    <br>
    <br>
    $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\
    \end{align}`$ \end{align}`$
    <br> <br>
    <br> <br>
    $`\begin{align} $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\ \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\ & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\
    $ =-\,\int_A^B \alpha\,d\phi_X \\ & =-\,\int_A^B \alpha\,d\phi_X \\
    <br> <br>
    <br> <br>
    $`\begin{align} $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\ \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\ & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\
    $ =-\,\int_A^B \alpha\,d\phi_X \\ & =-\,\int_A^B \alpha\,d\phi_X \\
    $ =-\,\int_A^B \mathcal{E}_X^{pot} \\ & =-\,\int_A^B \mathcal{E}_X^{pot} \\
    \\ \\
    & \color{brown}{\large{\mathbf{\;=-\,\mathcal{E}_X^{pot}(B)-\mathcal{E}_X^{pot}(A)}}}\\ & \color{brown}{\large{\mathbf{\;=-\,\mathcal{E}_X^{pot}(B)-\mathcal{E}_X^{pot}(A)}}}\\
    \end{align}`$ \end{align}`$
    ...@@ -568,8 +551,8 @@ $ =-\,\int_A^B \mathcal{E}_X^{pot} \\ ...@@ -568,8 +551,8 @@ $ =-\,\int_A^B \mathcal{E}_X^{pot} \\
    $`\begin{align} $`\begin{align}
    \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\ \displaystyle\color{brown}{\large{\mathbf{\displaystyle\int_A^B\overrightarrow{F}_{tot}\cdot\overrightarrow{dl}}}} & =\int_A^B \alpha\,\overrightarrow{X}\cdot\overrightarrow{dl}\\
    & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\ & =\int_A^B \alpha\,\big(-\,\overrightarrow{grad}\,\phi_X\big) \cdot\overrightarrow{dl} \\
    $ =-\,\int_A^B \alpha\,d\phi_X \\ & =-\,\int_A^B \alpha\,d\phi_X \\
    $ =-\,\int_A^B \mathcal{E}_X^{pot} \\ & =-\,\int_A^B \mathcal{E}_X^{pot} \\
    \\ \\
    & \color{brown}{\large{\mathbf{\;=-\,\mathcal{E}_X^{pot}(B)-\mathcal{E}_X^{pot}(A)}}}\\ & \color{brown}{\large{\mathbf{\;=-\,\mathcal{E}_X^{pot}(B)-\mathcal{E}_X^{pot}(A)}}}\\
    \\ \\
    ......
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