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5.5. SILE OVISNE O BRZINI: (2) LORENTZOVA SILA 123 Slika 5.7: Cikloide, odozgo prema dolje: obična, skraćena i produljena. 4 2 0 6 4 2 0 6 4 2 0 -2 0 50 100 150 200 Pokažimo da su jednadžbe za x i y iz (5.28) oblika jednadžba cikloide (5.29). Nazovimo Tada jednadžbe za x i y iz (5.28), glase ϕ = ωt − Φ. x(t) − v 0,y ω − E sin θ ω B Φ = E sin θ ϕ + R sin ϕ, ω B y(t) + v 0,x ω Uvedu li se nove (pomaknute) koordinate = E sin θ ωB + R cos ϕ. ˜x(t) = x(t) − v 0,y ω − E sin θ ω B Φ, ỹ(t) = y(t) + v 0,x ω , tada su gornje parametarske jednadžbe za ˜x(t) i ỹ(t) upravo oblika jednadžba cikloide (5.29) ˜x(t) = a ϕ + b sin ϕ, ỹ(t) = a + b sin ϕ, uz a ≡ E sin θ ω B , b ≡ −R.
124 POGLAVLJE 5. GIBANJE ČESTICE U POLJU KONSTANTNE SILE I SILA OVISNIH O BRZINI Sada se usporedba a i b svodi na usporedbu ili, ako su umjesto |ω| koristi T = 2π/|ω| E sin θ |ω| B R, E sin θ B 2 π R.
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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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174 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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412 POGLAVLJE 15. HAMILTONOVE JEDNA
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432 DODATAK A. DELTA FUNKCIJA sluč
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434 DODATAK A. DELTA FUNKCIJA Budu
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436 DODATAK A. DELTA FUNKCIJA
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438 DODATAK B. PRESJECI STOŠCA Sli
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440 DODATAK B. PRESJECI STOŠCA Za
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442 DODATAK B. PRESJECI STOŠCA jer
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444 DODATAK C. FOURIEROVI REDOVI za
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446 DODATAK C. FOURIEROVI REDOVI
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448 DODATAK D. VUČEDOLSKI KALENDAR
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450 DODATAK D. VUČEDOLSKI KALENDAR
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452 BIBLIOGRAFIJA [19] Kotkin G. L.
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454 KAZALO POJMOVA Steiner, Jakob,
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