# rachid mesrar appli cinetiqua.pdf

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#### Aperçu texte

r l &amp;r  
 l
r
&amp;
ψ
θ
d
sin
y
+ θx  

 2
r
 dV (G / R0 ) 
2 

Γ (G / R0 ) = 
 =
dt
dt

 R0 


R0
r
r
r l
l
dy 
l &amp;&amp;r l &amp;  dx 

&amp;
= (ψ&amp;&amp; sin θ + ψ&amp;θ cos θ ) y + ψ&amp; sin θ   + θx + θ  
2
2
2  dt  R0
 dt  R0 2

 r
 − ψ&amp; sin θ   0   − ψ&amp; cos θ 
r

   

r
d
y
 
&amp;

θ
=
(
R
/
R
)

y
=

1
=
0

0
  dt 
R0

 ψ&amp; cos θ   0   − ψ&amp; sin θ 

 − ψ&amp; sin θ   1   0 
r
  dxr 
   

r 
   = Ω ( R / R0 ) ∧ x =  θ&amp;
 ∧  0  = ψ&amp; cos θ 
 ψ&amp; cos θ   0   − θ&amp; 
  dt  R0

   

D’où :

r
r l
r l
r
l
Γ(G / R0 ) = (θ&amp;&amp; − ψ&amp; 2 sin θ cosθ ) x + (ψ&amp;&amp; sin θ + 2ψ&amp;θ&amp; cosθ ) y − (ψ&amp; 2 sin 2 θ + θ&amp; 2 ) z
2
2
2

Et

r
r
r
r
 dσ O (T / R0 ) 
 dσ O (T / R0 ) 
δ O (T / R0 ) = 
=
+

(
R
/
R
)

σ
0
O (T / R0 )



dt
dt

R0
R
r

r
r ml 2 &amp;&amp;
ml 2
 dσ O (T / R0 ) 
&amp;

 = − 3 (ψ&amp;&amp; sin θ + ψ&amp;θ cos θ ) x + 3 θy
dt
R
 ml 2
 

ml 2 &amp;
−
ψ&amp; sin θ   −
θψ&amp; cos θ 
3
 

 − ψ&amp; sin θ   3 2
2
r

r
ml
ml

2
Ω ( R / R0 ) ∧ σ O (T / R0 ) =  θ&amp;  ∧ 
θ&amp;  =  −
ψ&amp; sin θ cos θ 
3
3
 ψ&amp; cos θ  

0
0


 


 

__________________________________________________________________________________
Rachid MESRAR
Applications pédagogiques - Cinétique

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