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M3P2
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2124dad2
Commit
2124dad2
authored
May 19, 2024
by
Claude Meny
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Update 12.temporary_ins/40.classical-mechanics/30.n3/40.point-dynamics/20.overview/cheatsheet.fr.md
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cheatsheet.fr.md
...nics/30.n3/40.point-dynamics/20.overview/cheatsheet.fr.md
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12.temporary_ins/40.classical-mechanics/30.n3/40.point-dynamics/20.overview/cheatsheet.fr.md
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2124dad2
...
@@ -285,12 +285,12 @@ $`\hspace{0.5cm}\displaystyle\;=\dfrac{\sum_{i=1}^N d \overrightarrow{p}_{i\righ
...
@@ -285,12 +285,12 @@ $`\hspace{0.5cm}\displaystyle\;=\dfrac{\sum_{i=1}^N d \overrightarrow{p}_{i\righ
<br>
<br>
**$`
\h
space{0.5cm}
\L
arge
\m
athbf{
\;
=
\d
frac{d
\o
verrightarrow{p}_{tot
\r
ightarrow j}}{dt}}
`$**
**$`
\h
space{0.5cm}
\L
arge
\m
athbf{
\;
=
\d
frac{d
\o
verrightarrow{p}_{tot
\r
ightarrow j}}{dt}}
`$**
* La **quantité de mouvement totale** du
système isolé
des N corpuscules est la somme
* La **quantité de mouvement totale** du
*système isolé*
des N corpuscules est la somme
des quantités de mouvement de ses N corpuscules, soit :
des quantités de mouvement de ses N corpuscules, soit :
<br>
<br>
**$`
\d
isplaystyle
\L
arge
\m
athb
ƒ
{
\o
verrightarrow{p}_{sys.iso}}
`$**
**$`
\d
isplaystyle
\L
arge
\m
athb
f
{
\o
verrightarrow{p}_{sys.iso}}
`$**
*$`
\d
isplaystyle
\m
athb
ƒ
{
\;
=
\s
um_{i=1}^N
\o
verrightarrow{p}_{tot
\r
ightarrow j}}
`$*
*$`
\d
isplaystyle
\m
athb
f
{
\;
=
\s
um_{i=1}^N
\o
verrightarrow{p}_{tot
\r
ightarrow j}}
`$*
**$`
\d
isplaystyle
\L
arge
\m
athb
ƒ{
\
;
=
\s
um_{i=1}^N
\s
um_{j=1}^N
\o
verrightarrow{p}_{i
\r
ightarrow j}}
`$**
**$`
\d
isplaystyle
\L
arge
\m
athb
f{
;=
\s
um_{i=1}^N
\s
um_{j=1}^N
\o
verrightarrow{p}_{i
\r
ightarrow j}}
`$**
* La **dérivée temporelle de la quantité de mouvement totale** du système isolé s'exprime alors :
* La **dérivée temporelle de la quantité de mouvement totale** du système isolé s'exprime alors :
<br>
<br>
...
@@ -309,27 +309,7 @@ $`\displaystyle\hspace{0.5cm}=\sum_{i=1}^N \underbrace{\overrightarrow{F}_{i\rig
...
@@ -309,27 +309,7 @@ $`\displaystyle\hspace{0.5cm}=\sum_{i=1}^N \underbrace{\overrightarrow{F}_{i\rig
+
\s
um_{i=2}^N
\s
um_{j=1}^{(i-1)}
\u
nderbrace{
\b
ig(
\o
verrightarrow{F}_{i
\r
ightarrow j}
+
\s
um_{i=2}^N
\s
um_{j=1}^{(i-1)}
\u
nderbrace{
\b
ig(
\o
verrightarrow{F}_{i
\r
ightarrow j}
+
\o
verrightarrow{F}_{j
\r
ightarrow i}
\b
ig)}_{=
\,
0
\,
(action-réaction)}
`$
+
\o
verrightarrow{F}_{j
\r
ightarrow i}
\b
ig)}_{=
\,
0
\,
(action-réaction)}
`$
<br>
<br>
**$`
\L
arge
\m
athbf{
\h
space{0.5cm}=0}
`$**
**$`
\L
arge
\m
athbf{
\h
space{0.5cm}=0}
`
$
**
$`
\d
isplaystyle
\b
egin{align}
\d
frac{d
\o
verrightarrow{p}_{sys.iso}}{dt}&=
\d
frac{d
\b
ig(
\s
um_{i=1}^N
\s
um_{j=1}^N
\o
verrightarrow{p}_{i
\r
ightarrow j}
\b
ig)}{dt}
\\
\\
&=
\s
um_{i=1}^N
\s
um_{j=1}^N
\d
frac{d
\o
verrightarrow{p}_{i
\r
ightarrow j}}{dt}
\\
\\
&=
\s
um_{i=1}^N
\s
um_{j=1}^N
\o
verrightarrow{F}_{i
\r
ightarrow j}
\\
\\
&=
\s
um_{i=1}^N
\o
verrightarrow{F}_{i
\r
ightarrow i}
+
\s
um_{i=2}^N
\s
um_{j=1}^{(i-1)}
\o
verrightarrow{F}_{i
\r
ightarrow j}
+
\s
um_{j=2}^N
\s
um_{i=1}^{(j-1)}
\o
verrightarrow{F}_{i
\r
ightarrow j}
\\
\\
&=
\s
um_{i=1}^N
\u
nderbrace{
\o
verrightarrow{F}_{i
\r
ightarrow i}}_{=
\,
0}
+
\s
um_{i=2}^N
\s
um_{j=1}^{(i-1)}
\u
nderbrace{
\b
ig(
\o
verrightarrow{F}_{i
\r
ightarrow j}
+
\o
verrightarrow{F}_{j
\r
ightarrow i}
\b
ig)}_{=
\,
0
\,
(action-réaction)}
\\
\\
&=0
\e
nd{align}
`
$
<br>
<br>
Tu peux alors énoncer la loi de conservation :
Tu peux alors énoncer la loi de conservation :
<br>
<br>
...
...
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