rachid mesrar appli cinetiqua.pdf


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r l &r  
 l
r
&
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 &&r l &  dx 

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

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

   

r
d
y
 
&

θ
=
(
R
/
R
)

y
=

1
=
0






0
  dt 
R0







 ψ& cos θ   0   − ψ& sin θ 



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

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

   



D’où :

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

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

 − ψ& sin θ   3 2
2
r


r
ml
ml




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



0
0



 


 

__________________________________________________________________________________
Rachid MESRAR
Applications pédagogiques - Cinétique

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