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441 Slika B.3: Uz izvod jednadžbe parabole. Hiperbola se definira kao skup točaka u ravnini sa svojstvom da je razlika udaljenosti svake točke krivulje, P , od dvije fiksne točke (fokusa, O, O ′ ) konstantna (slika B.4) P O ′ − P O = 2a. Spustimo li se hiperbolom iz točke P u točku Q, gornja jednadžba postaje QO ′ − p = 2a. pomoću gornje relacije i trokuta △(O, O ′ , Q), dolazimo do izraza za p u obliku (2c) 2 + p 2 = QO ′2 = (2a + p) 2 , p = c2 a − a. Stavimo li u jednadžbu (B.3) za kut ϕ = 0, dobivamo ρ = OV = OC − CV = c − a, pri čemu je i d = V E. Sada iz definicije ekscentriciteta slijedi ɛ = ρ d = c − a V E S druge strane, za kut ϕ = 2 π u jednadžbi (B.3), dobivamo ⇒ V E = c − a . ɛ d = OE = OV + V E = c − a + V E, uz ρ = p. Ponovo iz ekscentriciteta dobivamo ɛ = ρ d = p c − a + V E ⇒ V E = p ɛ − c + a. Izjednačavanjem gornja dva izraza za V E, dobivamo (B.8) ɛ = c a > 1
442 DODATAK B. PRESJECI STOŠCA jer je c > a. Iz gornjeg izraza možemo c uvrstiti u (B.8) i dobiti što konačno vodi na jednadžbu hiperbole p = a(ɛ 2 − 1), ρ(ϕ) = a(ɛ2 − 1) 1 + ɛ cos ϕ . Nadalje se lako pokazuje da je mala poluos b = a √ ɛ 2 − 1, a položaj direktrise je x D = a(ɛ 2 −1)/ɛ. Prijelazom iz polarnih u pravokutne koordinate, kao kod elipse, dobivamo gornju jednadžbu u Slika B.4: Uz izvod jednadžbe hiperbole. obliku (x − ɛ a) 2 a 2 − y 2 a 2 (ɛ 2 − 1) = 1. Jedna grana hiperbole se dobije presjecanjem stošca ravninom okomitom na bazu stošca.
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KLASIČNA MEHANIKA UVOD Zvonko Glum
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Sadržaj 1 Uvod 1 I Mehanika jedne
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SADRŽAJ ix 9 Specijalna teorija re
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Ovo su bilješke s autorovih predav
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Predgovor Iz područja teorijske me
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Kazalo kratica i simbola ⃗A vekto
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Poglavlje 1 Uvod Na početku svake
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Naprotiv, snižavanjem temperature
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Dio I Mehanika jedne čestice 5
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8 POGLAVLJE 2. MATEMATIČKI UVOD -
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70 POGLAVLJE 3. KINEMATIKA Slika 3.
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72 POGLAVLJE 3. KINEMATIKA Ubrzanje
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74 POGLAVLJE 3. KINEMATIKA Prema sa
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76 POGLAVLJE 3. KINEMATIKA Slika 3.
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78 POGLAVLJE 3. KINEMATIKA
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80POGLAVLJE 4. NEWTONOVI AKSIOMI GI
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100POGLAVLJE 4. NEWTONOVI AKSIOMI G
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102 POGLAVLJE 5. GIBANJE ČESTICE U
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126POGLAVLJE 6. GIBANJE POD DJELOVA
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166 POGLAVLJE 7. GRAVITACIJA I CENT
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230 POGLAVLJE 8. INERCIJSKI I NEINE
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252 POGLAVLJE 9. SPECIJALNA TEORIJA
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Poglavlje 10 Sustavi čestica 10.1
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10.1. DISKRETNI I KONTINUIRANI SUST
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10.2. SREDIŠTE MASE 263 Uvedu li s
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10.3. KOLIČINA GIBANJA SUSTAVA ČE
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10.4. MOMENT KOLIČINE GIBANJA SUST
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10.5. ENERGIJA SUSTAVA ČESTICA 269
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10.5. ENERGIJA SUSTAVA ČESTICA 271
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10.6. GIBANJE SUSTAVA ČESTICA U OD
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10.6. GIBANJE SUSTAVA ČESTICA U OD
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10.8. LAGRANGEOVO I D’ALEMBERTOVO
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10.9. SUSTAVI S PROMJENJIVOM MASOM:
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10.9. SUSTAVI S PROMJENJIVOM MASOM:
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10.10. SUDARI ČESTICA 287 kao savr
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10.10. SUDARI ČESTICA 289 Pomoću
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10.10. SUDARI ČESTICA 291 Slika 10
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Poglavlje 11 Mali titraji sustava
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11.1. MALI LONGITUDINALNI TITRAJI J
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11.2. MALI TRANSVERZALNI TITRAJI KO
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11.3. TITRANJE PRAVOKUTNE MEMBRANE
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11.4. TITRANJE KRUŽNE MEMBRANE 329
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11.4. TITRANJE KRUŽNE MEMBRANE 331
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Poglavlje 12 Ravninsko gibanje krut
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12.2. MOMENT TROMOSTI 335 Slika 12.
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12.3. TEOREMI O MOMENTIMA TROMOSTI
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12.4. PAROVI SILA 339 Slika 12.6: U
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12.5. KINETIČKA ENERGIJA, RAD I SN
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12.5. KINETIČKA ENERGIJA, RAD I SN
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12.6. FIZIČKO NJIHALO 345 Slika 12
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12.6. FIZIČKO NJIHALO 347 postaje
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12.7. OPĆENITO RAVNINSKO GIBANJE K
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12.8. TRENUTNO SREDIŠTE VRTNJE 351
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12.8. TRENUTNO SREDIŠTE VRTNJE 353
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Poglavlje 13 Prostorno gibanje krut
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13.1. TENZOR TROMOSTI 357 što, ras
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13.1. TENZOR TROMOSTI 359 i tijelo
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13.1. TENZOR TROMOSTI 361 glavnih o
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13.1. TENZOR TROMOSTI 363 Slika 13.
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13.2. EULEROVE JEDNADŽBE GIBANJA 3
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13.3. GIBANJE ZEMLJE 367 Slika 13.5
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13.3. GIBANJE ZEMLJE 369 Vidimo da
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13.4. EULEROVI KUTOVI 371 Slika 13.
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13.4. EULEROVI KUTOVI 373 Lako je v
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13.5. GIBANJE ZVRKA 375 Slika 13.10
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13.5. GIBANJE ZVRKA 377 Ako na desn
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13.5. GIBANJE ZVRKA 379 Slika 13.11
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13.5. GIBANJE ZVRKA 381 postoje dva
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Dio III Analitička mehanika 383
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386 POGLAVLJE 14. LAGRANGEOVE JEDNA
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388 POGLAVLJE 14. LAGRANGEOVE JEDNA
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Page 425 and 426: 412 POGLAVLJE 15. HAMILTONOVE JEDNA
Page 445 and 446: 432 DODATAK A. DELTA FUNKCIJA sluč
Page 447 and 448: 434 DODATAK A. DELTA FUNKCIJA Budu
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Page 451 and 452: 438 DODATAK B. PRESJECI STOŠCA Sli
Page 453: 440 DODATAK B. PRESJECI STOŠCA Za
Page 457 and 458: 444 DODATAK C. FOURIEROVI REDOVI za
Page 459 and 460: 446 DODATAK C. FOURIEROVI REDOVI
Page 461 and 462: 448 DODATAK D. VUČEDOLSKI KALENDAR
Page 463 and 464: 450 DODATAK D. VUČEDOLSKI KALENDAR
Page 465 and 466: 452 BIBLIOGRAFIJA [19] Kotkin G. L.
Page 467: 454 KAZALO POJMOVA Steiner, Jakob,
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