KlasiÃ„Âna mehanika

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2.3. INTEGRAL VEKTORSKOG POLJA 21 Slika 2.8: Razlika ∆�r =�r2 −�r1 ima smjer sekante, a diferencijal d�r ima smjer tangente na krivulju C. Ako je C zatvorena krivulja (naravno, ne nuˇzno kruˇznica), linijski integral se označava kao � � � � �V d�r = Vxdx+ Vydy + Vzdz. (2.15) Povrˇsinski integral: Na sličan se način definira i povrˇsinski integral vektorskog polja (slika 2.9) Slika 2.9: Uz definiciju povrˇsinskog integrala vektorskog polja, (2.16). � S �V d � S, (2.16)
22 POGLAVLJE 2. MATEMATIČKI UVOD - ELEMENTI VEKTORSKOG RAČUNA gdje je d � S vektor kojemu je iznos jednak diferencijalu plohe dS, a smjer je dan okomicom 4 na taj isti diferencijal plohe d � S = dS �n0, gdje je �n0 jedinični vektor okomit na element dS. Dakle, skalarnim umnoˇskom � V d � S se u svakoj točki plohe računa komponeta polja okomita na malu okolicu promatrane točke �V d � S = V⊥ dS V⊥ = � V ·�n0. Vrijednosti svih tih okomitih komponenata se zbrajaju po svim točkama plohe i rezultat je gornji povrˇsinski integral. Primjetimo joˇs da za svaku plohu dS postoje dva okomita vektora, �n0 i −�n0, pa u računima treba paziti s kojim se od ta dva vektora računa. Ako se radi o zatvorenoj plohi, integral se označava kao � �V d � S, a smjer d � S je iz unutraˇsnjosti plohe prema van. Gornji se izrazi mogu raspisati i u pravokutnim koordinatama gdje su S �n0 = (�n0 ·�ex)�ex +(�n0 ·�ey)�ey +(�n0 ·�ez)�ez, = cos(�n0,�ex)�ex +cos(�n0,�ey)�ey +cos(�n0,�ez)�ez, � dS �n0 = dS cos(�n0,�ex)�ex +cos(�n0,�ey)�ey +cos(�n0,�ez)�ez = dSx�ex +dSy�ey +dSz�ez, � S �V d � � S = dSx = dS cos(�n0,�ex), dSy = dS cos(�n0,�ey), dSz = dS cos(�n0,�ez). S � VxdSx + S � VydSy + S VzdSz, Primjetimo da je obični integral vektorskog polja, opet neki vektor kao npr. (2.12), (2.13) ili (2.14), dok su linijski (2.15) i povrˇsinski integrali (2.16), po svom algebarskom karakteru skalari. 4 Sama ploha S po kojoj se integrira, nipoˇsto ne mora biti ravnina, ali diferencijal dS se uvijek smatra toliko malenim da se jako dobro aproksimira ravninom i zato je na tu ravninu moguće definirati okomicu. � ,
Page 1 and 2: KLASIČNA MEHANIKA UVOD Zvonko Glum
Page 4 and 5: Sadrˇzaj 1 Uvod 1 I Mehanika jedne
Page 6 and 7: SADR ˇ ZAJ ix 8.3.4 Kosi hitac . .
Page 8 and 9: SADR ˇ ZAJ xi 16 Mali titraji sust
Page 10 and 11: Ovo su biljeˇske s autorovih preda
Page 12 and 13: Predgovor Iz područja teorijske me
Page 14 and 15: Kazalo kratica i simbola �A vekto
Page 16 and 17: Poglavlje 1 Uvod Na početku svake
Page 18 and 19: nego imaju i valna svojstva (kao ˇ
Page 20: Dio I Mehanika jedne čestice 5
Page 23 and 24: 8 POGLAVLJE 2. MATEMATIČKI UVOD -
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72 POGLAVLJE 2. MATEMATIČKI UVOD -
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92 POGLAVLJE 3. KINEMATIKA Slika 3.
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94 POGLAVLJE 3. KINEMATIKA Prvi čl
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96 POGLAVLJE 3. KINEMATIKA Slika 3.
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98 POGLAVLJE 3. KINEMATIKA Prva od
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100 POGLAVLJE 3. KINEMATIKA iz čeg
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102POGLAVLJE4. NEWTONOVIAKSIOMIGIBA
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126 POGLAVLJE 5. GIBANJE ČESTICE U
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152 POGLAVLJE 6. HARMONIJSKI OSCILA
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204 POGLAVLJE 7. GRAVITACIJA I CENT
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270 POGLAVLJE 8. INERCIJSKI I NEINE
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294 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. SREDI ˇ STE MASE 307 Slika 1
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10.2. SREDI ˇ STE MASE 309 Sa slik
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10.3. KOLI ČINAGIBANJA,MOMENTKOLI
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10.4. NEINERCIJSKI KOORDINATNI SUST
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10.4. NEINERCIJSKI KOORDINATNI SUST
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10.5. LAGRANGEOVO I D’ALEMBERTOVO
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10.6. SUSTAVI S PROMJENJIVOM MASOM:
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10.6. SUSTAVI S PROMJENJIVOM MASOM:
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10.7. SUDARI ČESTICA 341 Zadatak:
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10.7. SUDARI ČESTICA 343 R: Prema
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10.7. SUDARI ČESTICA 345 i poslije
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10.7. SUDARI ČESTICA 347 Slika 10.
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10.7. SUDARI ČESTICA 349 R: dovrˇ
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Poglavlje 11 Mali titraji sustava
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11.1. MALILONGITUDINALNITITRAJIJEDN
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11.2. MALITRANSVERZALNITITRAJIKONTI
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11.3. TITRANJE PRAVOKUTNE MEMBRANE
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11.4. TITRANJE KRU ˇ ZNE MEMBRANE
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11.5. TITRANJE MOLEKULA 401 Slika 1
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Poglavlje 12 Ravninsko gibanje krut
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12.2. MOMENT TROMOSTI KRUTOG TIJELA
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12.3. TEOREMI O MOMENTIMA TROMOSTI
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12.4. PAROVI SILA 413 izaziva trans
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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 419 Slika 12
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12.6. FIZIČKO NJIHALO 421 Izračun
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12.6. FIZIČKO NJIHALO 423 Uvrstiv
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12.7. OPĆENITO RAVNINSKO GIBANJE K
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12.8. TRENUTNO SREDI ˇ STE VRTNJE
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12.8. TRENUTNO SREDI ˇ STE VRTNJE
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12.9. STATIKA KRUTOG TIJELA 431 Uvj
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12.9. STATIKA KRUTOG TIJELA 433 Sad
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12.9. STATIKA KRUTOG TIJELA 435 Zad
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12.9. STATIKA KRUTOG TIJELA 437 Pro
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Poglavlje 13 Prostorno gibanje krut
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13.1. TENZOR TROMOSTI 441 komponent
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13.1. TENZOR TROMOSTI 443 njegove s
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13.1. TENZOR TROMOSTI 445 Uvrstimo
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13.1. TENZOR TROMOSTI 447 glavnih o
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13.2. EULEROVE JEDNAD ˇ ZBE GIBANJ
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13.2. EULEROVE JEDNAD ˇ ZBE GIBANJ
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13.3. GIBANJE ZEMLJE 453 Eulerove j
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13.3. GIBANJE ZEMLJE 455 (glavne os
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13.4. EULEROVI KUTOVI 457 13.4 Eule
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13.4. EULEROVI KUTOVI 459 Iz gornje
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13.5. CAYLEY - KLEIN PARAMETRI 461
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13.6. GIBANJE ZVRKA 463 sustav d
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13.6. GIBANJE ZVRKA 465 Integracijo
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13.6. GIBANJE ZVRKA 467 Slika 13.10
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13.6. GIBANJE ZVRKA 469 odeduju rub
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13.6. GIBANJE ZVRKA 471 Slika 13.13
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Dio III Analitička mehanika 473
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476 POGLAVLJE 14. LAGRANGEOVE JEDNA
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510 POGLAVLJE 15. HAMILTONOVE JEDNA
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554 POGLAVLJE 16. MALI TITRAJI SUST
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556 POGLAVLJE 16. MALI TITRAJI SUST
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558 POGLAVLJE 17. KLASIČNA TEORIJA
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Poglavlje 18 Mehanika Fluida uvodni
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Dodatak A Matematički dodatak A.1
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A.2. TAYLOROV RAZVOJ 583 A.2 Taylor
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A.4. ZAOKVIRENE FORMULE IZ OVE KNJI
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Dodatak B Diracova δ-funkcija Dira
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Sli”cnim se postupkom dobije i
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Na sli”can na”cin, u sfernom ko
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Dodatak C Presjeci stoˇsca: kruˇz
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Elipsa se definira kao ravninska kr
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Slika C.3: Uz izvod jednadˇzbe par
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Dodatak D Elementi Fourierove anali
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Izračunajmo sada integral IN ako u
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Dodatak E Vučedolski kalendar http
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već kao kanon stoji na tom prijelo
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Bibliografija [1] Aganović I., Ves
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Kazalo autora Bessel, FriedrichWilh
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Kazalo pojmova mehanicizam, 205 amp
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KAZALO POJMOVA 613 laplasijan, 46 L
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KAZALO POJMOVA 615 teorem Gaussov,
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