MECANIQUE RATIONNELLE

Recommendations

Info

UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 A.KADI → z 0 → z 2 θ → → z 0 ≡ z 1 → x 0 A O G B → y 0 → x 0 A O θ ψ G B → y 1 → x 1 → y → x 2 1 → y → y 2 0 Solution : 1. Repères et paramètres permettant l’étude du mouvement de la tige AB = L ; → A ∈ O, z ) tous le temps, B ∈ x 0 Oy ) ( 0 ( 0 → → → 0 ( 0 0 0 R x , y , z ) : repère fixe ; → → → 1( 1 1 1 → → 0 ≡ z 1 → → → → 0 , 1 0 y1 R x , y , z ) un repère tel que : z , ( x x ) = ( y , ) = ψ et → → → 2 ( 2 2 2 → → 1 ≡ y 2 → → → → x1, x2 ) = ( z1, z2 R x , y , z ) un repère tel que : y , ( ) = ψ et → • → • → 0 Ω1 ≡ψ z0 = ψ z1 → • → • → 1 Ω 2 ≡ −θ y1 = −θ y2 on a ainsi : AB ∈ R 2 tel que : −→ BA L z → = 2 Les deux angles ψ et θ sont suffisant pour décrire entièrement le mouvement de la barre par rapport au repère R 0 . 2. Vitesse instantanée de rotation de la barre par rapport à R0 Nous avons : → 0 Ω 2 → 1 2 ≡ Ω → 0 1 + Ω • → ≡ −θ y 1 ⎧ 0 • → • ⎪ 1= ⎨−θ • ⎪ R ⎩ ψ 1 + ψ z 265
UMBB Boumerdès, Faculté des sciences, Département de physique Cours exercices, Mécanique Rationnelle : TCT et LMD-ST sem :3 A.KADI 3. Figure plane de chaque repère ; 3.1. Matrice de passage du repère R0 vers R1 Matrice de passage de R vers R1 0 → y 1 → ⎛ ⎞ ⎜ x0 ⎟ ⎛cosψ ⎜ → ⎟ ⎜ ⎜ y0 ⎟ = ⎜ sinψ → ⎜ ⎟ ⎜ z0 ⎝ 0 ⎝ ⎠ − sinψ cosψ 0 ⎛ 0⎞⎜ x ⎟⎜ 0⎟⎜ y 1⎟⎜ ⎠ z ⎝ → 1 → 1 → 1 ⎞ ⎟ ⎟ ⎟ ⎟ ⎠ P R 0→ R 1 → → z 0 ≡ z 1 O → x 0 ψ ψ → x 1 → y 0 3.1. Matrice de passage du repère R2 vers R1 ⎛ ⎜ x ⎜ ⎜ y ⎜ z ⎝ → 0 Ω 2 → 2 → 2 → 2 → ⎞ ⎛ ⎞ ⎟ ⎛ cosθ 0 sinθ ⎞⎜ x1 ⎟ ⎜ ⎟⎜ → ⎟ = ⎜ 0 1 0 ⎟⎜ y1 ⎟ ⎜ ⎟ → ⎜ ⎝− sinθ 0 cosθ ⎠ z ⎟ ⎟⎟⎟⎟ 1 ⎠ ⎝ ⎠ P R 2→ R 1 • → ≡ −θ y 1 • → + ψ z 1 • → → • → ( 0 + cosψ y0 ) + ψ z0 = −θ −sinψ x → → B y 1 ≡ y 2 → x 1 θ • ⎧ ⎪ θ sinψ • = ⎨−θ cosψ • ⎪ ⎪ ψ R ⎩ 0 θ → x 2 → z 2 → z 1 On prendra R 1 comme repère de projection car les expressions cinématiques sont plus simples dans ce repère. 4. Vitesse et Accélération absolue des points A, B et G exprimé R 1 . ⎧ 0 ⎧Lsinθ −→ −→ ⎪ ⎪ Nous avons : OA= ⎨ 0 , OB = ⎨ 0 , ⎪ R ⎩L cosθ ⎪ R ⎩ 0 1 1 ⎧ L −→ −→ ⎪ sinθ −→ OA+ OB 2 OG = = ⎪ ⎪ ⎨ 0 2 L cosθ R ⎩ 2 1 → 0 4.1. calcul de V (A) : 1 → 0 V 1 −→ −→ 0 1 → d OA d OA −→ 0 ( A) = = + Ω1 ∧ OA dt dt ⎧ 0 ⎧0 ⎧ 0 → 0 ⎪ ⎪ ⎪ V ( A) = ⎨ 0 + ⎨0∧ ⎨ 0 = • • ⎪ ⎪ ⎪ R ⎩− Lθ sinθ R ⎩ψ R ⎩L cosθ 1 ⎧ 0 ⎪ ⎨ 0 • ⎪ R ⎩− Lθ sinθ 1 266
Page 1 and 2:
CLASSES PREPARATOIRES AUX GRANDES E
Page 3 and 4:
Préface Quand Ali KADI m’a amica
Page 5 and 6:
UMBB Boumerdès, Faculté des scien
Page 7 and 8:
Page 9 and 10:
Page 11 and 12:
Page 13 and 14:
Page 15 and 16:
Page 17 and 18:
Page 19 and 20:
Page 21 and 22:
Page 23 and 24:
Page 25 and 26:
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Page 71 and 72:
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Page 153 and 154:
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Page 171 and 172:
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
Page 191 and 192:
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Page 209 and 210:
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218: UMBB Boumerdès, Faculté des scien
Page 267: UMBB Boumerdès, Faculté des scien
Page 319 and 320:
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
Page 335 and 336:
Page 337 and 338:
Page 339 and 340:
Page 341 and 342:
Page 343 and 344:
Page 345 and 346:
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
Page 355 and 356:
Page 357 and 358:
Page 359 and 360:
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
Page 383 and 384:
Page 385 and 386:
Page 387 and 388:
Page 389 and 390:
Page 391 and 392:
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
Page 409 and 410:
Page 411 and 412:
Page 413 and 414:
show all

MECANIQUE RATIONNELLE

Create successful ePaper yourself

Delete template?

Save as template?