Materialverhalten anisotroper Festkörper: Thermische und by Professor Dr. rer. nat. Wolfgang Dreyer (auth.)

By Professor Dr. rer. nat. Wolfgang Dreyer (auth.)

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Additional resources for Materialverhalten anisotroper Festkörper: Thermische und elektrische Eigenschaften Ein Beitrag zur Angewandten Mineralogie

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45 sin 2 l? (cos l? )= 90 sin l? (cos l? ) = 90 (cos l? ) = - y. )= - 105 sin 3 l? cos l? ) = 105 sin 4 l? (417) + 1)2 (396) l? (5 cos 2 l? - 3) 4 (397) (398) 1) (399) (400) (401) 1) 2 l? - 10 cos l? - 1) + 1) (403) (404) + 1)2 + 1) (411) 1)2 l? - 30 cos 2 l? (407) (410) (412) + 3) sin l? cos l? (7 cos 2 l? - 3) 2 (402) l? (7 cos 2 l? 15. Verallgemeinerte Zuordnung P411(~)= t sin ~ cos ~ (7 cos 2 ~ - 3) i- (cos ~ + 1) (28 COS3~ - 21 cos2 ~ - P412(~)= - 15 sin P413(~)= 105 P414(~)= - 420 sin 3 ~ (cos P410 (~)= P 420 (~) = P 421 (~)= (cos sin2~ ~ sin2~ 2 15 sin (cos ~ + 1) (14 ~ (7 COS2~ + 1) (4 cos ~ ~ ~ -7 cos (423) 1) (14 cos 2 ~ - 7 cos ~ - 1) P 423 (~) = - 630 sin ~ (2 cos ~ - 1) (cos ~ + 1)2 P 424 (~) = P430(~)= 105 cos P431(~)= 105 sin 2 ~ (cos P 432 (~)= 630 sin sin3~ ~ (cos ~ ~ + 1) + 1)2 (424) (425) (426) (427) (428) ~ ~ (2 cos (420) (422) + 1) + 1)2 (7 cos 2 ~ - 7 cos ~ - 1) (419) (421) = 1260 sin2 ~ - 1) P 422 (~) ~ 6 cos ~ + 3) - 1) COS2~ ~ ( cos ~ + 90 (cos (418) + 1) (4 cos ~ - 1) (429) - 1) (cos ~ + 1)2 (430) ~ P 433 (~) = 630 (4 cos ~ - 3) (cos ~ + 1)3 (431) P 434 (~) = - 2520 sin ~ (cos ~ + (432) P 440 (~) = P 441 (~)= 1)3 (433) 105sin4~ 420 sin3 ~ (cos ~ (434) + 1) P 442 (~) = P 443 (~) = 2520 sin ~ (cos ~ + 1)3 (436) P 444 (~) = 2520 (cos ~ + 1)4 (437) 1260 sin2~ (cos ~ + 1)2 (435) Die verallgemeinerte Zuordnung hat die Integraleigenschaft: 11 f P~m 1 (~).

N-m)! 2(2n-l) (n-m) (n-m-l) (n-m-2) (n-m-3)· n m . COS • -4 ~ + ... 2 . 4 . (2n-l) (2n-3) 1 (248) Pie Definition (246) und die Entwicklung (248) gilt nur ftiT die Bedingung m ~ n, d. h. der Index m mu~ stets kleiner oder darf h6chstens gleich n sein. Setzt man in (248) flir m den Wert Null ein, folgt (204), so gilt. Speziell erhiilt man: Poo (~)= 1 da~ auch hier (247) (249) (250) P ll (~) = sin ~ P 20 (~)=+ (3 COS2~ -1) (251) (252) 40 2. 12. Zugeordnete Kugelfunktionen 41 Fiihrt man statt der Potenzen der trigonometrischen Funktionen die Vielfachen des Winkels iJ ein, folgt: P20 (iJ) =-{- (l + 3 cos 2 iJ) (277) P 21 (iJ) =+ sin 2 iJ (278) P22 (iJ) =+ (l (279) P 30 (iJ) =t (3 cos iJ + 5 cos 3 iJ) (280) P 31 (iJ) =i (sin iJ + 5 sin 3 iJ) (281) P 32 (iJ) 15 ="4 (cos iJ - P 33 (iJ) =1f (3 sin iJ - P 40 (iJ) =b.

15 sin 3 l? ) = 1- sin l? (5 cos 2l? )= 1- (cos l? )= - 15 sin l? (cos l? + 1) (3 cos l? )= 45 sin 2 l? (cos l? ) = 15 sin 2 l? cos l? )= 15 sin l? (cos l? + 1) (3 cos l? ) = 30 (3 cos l? - 2) (cos l? ) = - 90 sin l? (cos l? )= 15 sin 3 l? )= 45 sin 2 l? (cos l? )= 90 sin l? (cos l? ) = 90 (cos l? ) = - y. )= - 105 sin 3 l? cos l? ) = 105 sin 4 l? (417) + 1)2 (396) l? (5 cos 2 l? - 3) 4 (397) (398) 1) (399) (400) (401) 1) 2 l? - 10 cos l? - 1) + 1) (403) (404) + 1)2 + 1) (411) 1)2 l? - 30 cos 2 l?

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