MECANIQUE RATIONNELLE

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UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 A.KADI → 0 4.2. calcul de V ( B) → 0 V → 0 V −→ −→ 0 1 → d OB d OB −→ 0 ( B) = = + Ω1 ∧ OB dt dt • ⎧ ⎧ ⎧ ⎪ Lθ cosθ 0 Lsinθ ⎪ ⎪ ( B) = ⎨ 0 + ⎨0∧ ⎨ 0 = • ⎪ 0 ⎪ ⎪ ⎪ ⎩ψ ⎩ 0 ⎩ R1 R1 R 1 • ⎧ ⎪ Lθ cosθ • ⎨Lψ sinθ ⎪ 0 R ⎪⎩ 1 La vitesse du point B peut aussi s’obtenir à partir de celle de A par la cinématique du solide : → 0 V → 0 → 0 2 −→ ( B) = V ( A) + Ω ∧ AB → 0 V ( B) = • • ⎧ ⎧ ⎧ 0 ⎧ 0 ⎧ Lsinθ ⎪ Lθ cosθ ⎪ Lθ cosθ • • • ⎪ ⎪ ⎪ ⎨ 0 + ⎨−θ ∧ ⎨ 0 = ⎨ Lψ sinθ = ⎨Lψ sinθ • • • • ⎪ ⎪ ⎪ ⎪ ⎪ R ⎩− Lθ sinθ ⎩ ψ ⎩− cosθ ⎪− θ sinθ + θ sinθ 0 1 R R L L L 1 1 R ⎩ R ⎪⎩ 1 1 → 0 4.3. calcul de V ( G) : → 0 V → 0 V −→ ⎧ L • ⎧ L ⎪ θ cosθ ⎧0 ⎪ sinθ 2 ⎪ 2 ( G) = ⎨ 0 + ⎨0 ∧ ⎨ 0 = • • ⎪ L − θ sinθ ⎪ ⎪L ⎪ ⎩ψ cosθ ⎪ ⎩ 2 R1 R R ⎩ 2 1 −→ 0 1 → d OG d OG −→ 0 ( G) = = + Ω1 ∧ OG dt dt 1 ⎧ L • ⎪ θ cosθ 2 ⎪ L • ⎨ ψ sinθ ⎪ 2 • ⎪ L − θ sinθ R ⎪⎩ 2 La vitesse du point G peut aussi s’obtenir à partir de celle de A où de B par la cinématique du solide, en effet nous avons : → 0 V → 0 → 0 2 −→ ( G) = V ( A) + Ω ∧ AG 1 → 0 V ( G) = ⎧ L • ⎧ L ⎪ θ cosθ ⎧ 0 ⎧ 0 ⎪ sinθ 2 • ⎪ ⎪ 2 ⎪ L • ⎨ 0 + ⎨−θ ∧ ⎨ 0 = ⎨ ψ sinθ = • • ⎪ ⎪ ⎪ L − ⎪ 2 ⎩− θ θ • • R L sin ⎩ ψ cosθ 1 R ⎪ ⎪ L 1 R ⎩ 2 − Lθ sinθ + θ sinθ 1 R ⎪⎩ 2 1 ⎧ L • ⎪ θ cosθ 2 ⎪ L • ⎨ ψ sinθ ⎪ 2 • ⎪ L − θ sinθ R ⎪⎩ 2 1 267
UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 268 A.KADI 4.4. calcul de : (A) 0 → γ A V dt A V d dt A V d A 1 0 ) ( ) ( ) ( ) ( 0 0 1 0 0 0 → → → → → ∧ + Ω = = γ ⎪ ⎩ ⎪ ⎨ ⎧ − − = ⎪ ⎩ ⎪ ⎨ ⎧ − ∧ ⎪ ⎩ ⎪ ⎨ ⎧ + ⎪ ⎩ ⎪ ⎨ ⎧ − − = • •• • • • •• → θ θ θ θ θ θ ψ θ θ θ θ cos sin 0 0 sin 0 0 0 0 cos sin 0 0 ) ( 2 1 1 1 2 1 0 L L R L R R L L R A V 4.5. calcul de : (B) 0 → γ ) ( ) ( ) ( ) ( 0 0 1 0 0 0 B V dt B V d dt B V d B 1 0 → → → → → ∧ + Ω = = γ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ∧ ⎪ ⎩ ⎪ ⎨ ⎧ + ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + − = • • • • • •• • •• → 0 sin cos 0 0 0 cos sin sin cos ) ( 1 1 2 1 0 θ ψ θ θ ψ θ ψ θ θ ψ θ θ θ θ L L R R L L L L R B V ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ + + − = • • •• • • •• → 0 cos 2 sin )sin ( cos ) ( 2 2 1 0 θ ψ θ θ ψ θ ψ θ θ θ L L L L L R B V 4.6. calcul de : (G) 0 → γ ) ( ) ( ) ( ) ( 0 0 1 0 0 0 G V dt G V d dt G V d G 1 0 → → → → → ∧ + Ω = = γ ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ − ∧ ⎪ ⎩ ⎪ ⎨ ⎧ + ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ − − + − = • • • • • •• • • •• • •• → θ θ θ ψ θ θ ψ θ θ θ θ θ ψ θ θ ψ θ θ θ θ γ sin 2 sin 2 cos 2 0 0 cos 2 sin 2 cos 2 sin 2 sin 2 cos 2 ) ( 1 1 2 2 1 0 L L L R R L L L L L L R B L L L L L L L R B ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ − − + − − = • •• • • •• • • •• → θ θ θ θ θ ψ θ θ ψ θ ψ θ θ θ θ γ cos 2 sin 2 cos sin 2 sin 2 sin 2 cos 2 ) ( 2 2 2 1 0
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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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