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M3P2
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e0cd1585
Commit
e0cd1585
authored
Aug 30, 2020
by
Claude Meny
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Update textbook.fr.md
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00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md
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e0cd1585
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@@ -406,24 +406,24 @@ la longueur infinitésimale $`dl_{\varphi}`$ parcourue pour le point $`M`$ est :
continuously between the values $
`\varphi`
$ and $
`\varphi+\Delta \varphi`
$, the point $
`M`
$ covers
an arc of circle of length $
`\Delta l_{\varphi}=\rho\.\Delta \varphi`
$. When $
`\Delta \varphi`
$ tends
towards $
`0`
$, the infinitesimal length $
`dl_{\varphi}`
$ covered by the point $
`M`
$ is :
<br>
<br>
$
`\displaystyle d\varphi=\lim_{\Delta \varphi\rightarrow 0 \\ \Delta \varphi>0} \Delta
\varphi`
$
$
`\quad\Longrightarrow\quad dl_{\phi}=\rho\,d
÷
phi`
$.
<br>
<br>
$
`\displaystyle d\varphi=\lim_{\Delta \varphi\rightarrow 0 \\ \Delta \varphi>0} \Delta\varphi`
$
$
`\quad\Longrightarrow\quad dl_{\phi}=\rho\,d
\var
phi`
$.
<br>
*
**N3 ($`\rightarrow`$ N4)**
<br>
[
ES
]
Cuando solo la coordenada $
`\rho`
$ de un punto $
`M(\rho, \varphi, z)`
$ aumenta
infinitesimalmente entre los valores $
`\rho`
$ y $
`\rho+d\rho`
$ ($
`d\rho>0`
$)
para llegar al punto $
`M'(\rho+\
d
elta\rho, \varphi, z)`
$, el vector de desplazamiento
para llegar al punto $
`M'(\rho+\
D
elta\rho, \varphi, z)`
$, el vector de desplazamiento
$
`\overrightarrow{MM'}=\partial\overrightarrow{OM}_{\rho}`
$ del punto $
`M`
$ el vector
tangente a la trayectoria en el punto $
`M`
$ que se escribe :
<br>
[
FR
]
Lorsque seule la coordonnées $
`\rho`
$ d'un point $
`M(x,y,z)`
$ s'accroît de façon
infinitésimale entre les valeurs $
`\rho`
$ et $
`\rho+d\rho`
$ ($
`d\rho>0`
$)
pour atteindre le point $
`M'(\rho+\
d
elta\rho, \varphi, z)`
$, le vecteur déplacement
pour atteindre le point $
`M'(\rho+\
D
elta\rho, \varphi, z)`
$, le vecteur déplacement
$
`\overrightarrow{MM'}=\partial\overrightarrow{OM}_{\rho}`
$ du point $
`M`
$ est le vecteur
tangent à la trajectoire au point $
`M`
$ qui sc'écrit :
<br>
When only the $
`\rho`
$ coordinate of a point $
`M(x,y,z)`
$ increases infinitesimally between
the values $
`\rho`
$ and $
`\rho+d\rho`
$ ($
`d\rho>0`
$) to reach the point
$
`M'(\rho+\
d
elta\rho, \varphi, z)`
$, the displacement vector
$
`M'(\rho+\
D
elta\rho, \varphi, z)`
$, the displacement vector
$
`\overrightarrow{MM'}=\partial\overrightarrow{OM}_{\rho}`
$ of the point $
`M`
$ is the
tangent vector to the trajectory at point $
`M`
$. It writes :
<br>
<br>
$
`\overrightarrow{MM'}=\partial\overrightarrow{OM}_{\rho}=\dfrac{\partial \overrightarrow{OM}}{\partial \rho}\cdot d\rho`
$
<br>
...
...
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