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UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 275 A.KADI ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − − = ⎪ ⎩ ⎪ ⎨ ⎧ ∧ ⎪ ⎩ ⎪ ⎨ ⎧ − = ∧ + Ω = • • • • • • −→ → → → cos sin cos cos sin cos sin sin cos cos sin 0 ) ( ) ( 2 2 2 0 2 0 0 2 θ β ψ θ β ψ θ β ψ β ψ θ θ β ψ β ψ R R R h R h R R R R OM O V M V ce qui donne : ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + − − − = • • • • • • → R R R R R h R M V θ β ψ θ θ θ β ψ θ θ θ β ψ β ψ cos sin cos cos cos sin sin cos sin ) ( 2 0 3.2 Accélération : Nous avons : , ) ( ) ( ) ( ) ( 0 2 2 0 M M M M c → → → → + + = γ γ γ γ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − − = = • • → → R R R dt M V d M 0 sin cos ) ( ) ( 2 2 2 2 2 2 θ θ θ θ γ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∧ Ω ∧ + Ω ∧ Ω + = −→ → → −→ → → → OM OM dt d O M 0 2 0 2 0 2 0 0 0 2 ) ( ) ( γ γ ; avec : → → = 0 ) ( 0 O γ → → → → → = ∧ Ω + Ω Ω = Ω 0 0 2 0 2 0 2 2 0 2 0 dt d dt d ⎪ ⎩ ⎪ ⎨ ⎧ ∧ ⎪ ⎩ ⎪ ⎨ ⎧ − ∧ ⎪ ⎩ ⎪ ⎨ ⎧ − ⎟= ⎠ ⎞ ⎜ ⎝ ⎛ ∧ Ω ∧ Ω • • • • −→ → → h R R R R R OM θ θ β ψ β ψ β ψ β ψ sin cos cos sin 0 cos sin 0 2 2 2 0 2 0 2 ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − − ∧ ⎪ ⎩ ⎪ ⎨ ⎧ − ⎟= ⎠ ⎞ ⎜ ⎝ ⎛ ∧ Ω ∧ Ω • • • • • • −→ → → R R R h R R OM θ β ψ θ β ψ θ β ψ β ψ β ψ β ψ cos sin cos cos sin cos sin cos sin 0 2 2 0 2 0 2
UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 A.KADI → → ⎛ −→ 0 0 Ω 2 ∧ ⎜Ω 2 ∧ OM ⎝ ⎞ ⎟= ⎠ • ⎧ 2 ⎪− Rψ cosθ • ⎪ 2 ⎨ −ψ cos β • ⎪ 2 ⎪ −ψ sin β R ⎩ 2 ( hsin β + R cos β sinθ ) ( hsin β + R cos β sinθ ) → γ ( M ) = 2 c → ⎛ 0 ⎜Ω 2 ∧V ⎝ → 2 ⎞ ( M ) ⎟= ⎠ R 2 ⎧ 0 ⎪ • ⎨−ψ sin • ⎪ ⎩ ψ cos β β ∧ • ⎧ ⎪ − Rθ sinθ • ⎨ Rθ cosθ ⎪ 0 R ⎪⎩ 2 = • • ⎧ ⎪ − 2Rθ ψ cosθ cos β • • ⎨− 2Rθ ψ sinθ cos β • • ⎪ ⎪ − 2Rθ ψ sinθ sin β R ⎩ 2 La somme de toutes ces expressions donne : • • ⎧ ⎛ • • 2 2 ⎞ ⎪− R cosθ ⎜θ + ψ + 2Rθ ψ cos β ⎟ ⎪ ⎝ ⎠ → • • ⎪ ⎛ • • 0 2 2 ⎞ γ ( M ) = ⎨−ψ cos β ( hsin β + R cos β sinθ ) − Rsinθ ⎜θ + 2Rθ ψ cos β ⎟ ⎪ ⎝ ⎠ • • • ⎪ 2 ⎪−ψ sin β ( hsin β + R cos β sinθ ) − 2Rθ ψ sinθ sin β R ⎩ 2 276
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CLASSES PREPARATOIRES AUX GRANDES E
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Préface Quand Ali KADI m’a amica
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UMBB Boumerdès, Faculté des scien
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MECANIQUE RATIONNELLE

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