Dyadic representation papp+pap中+paaz2 +apP+φaφ+oasz2+ +2ap+22中+2az2 (D.50) a=pa+a+ia=app+a,+a2 (D.51) a=ap+a中+a92 a2=ap+a中+a2 (D.57) Differential operations pdp dv= pdpdo dz (D.59) dSp=pdφd dSo= dp dz, (D.61) Vf=pa +6+ (D.63) 1a(PFp)+p a 1aF。,aF2 V×F 能 (D65) a-f f 2 d VF=PV2Fp +中(VFaE9 +2v2F2(D.67) @2001 by CRC Press LLCDyadic representation a¯ = ρˆ aρρρˆ + ρˆ aρφφˆ + ρˆ aρzzˆ + + φˆ aφρρˆ + φˆ aφφφˆ + φˆ aφzzˆ + + zˆazρρˆ + zˆazφφˆ + zˆazzzˆ (D.50) a¯ = ρˆ a ρ + φˆ a φ + zaˆ  z = aρρˆ + aφφˆ + azzˆ (D.51) a ρ = aρρρˆ + aρφφˆ + aρzzˆ (D.52) a φ = aφρρˆ + aφφφˆ + aφzzˆ (D.53) a z = azρρˆ + azφφˆ + azzzˆ (D.54) aρ = aρρρˆ + aφρφˆ + azρzˆ (D.55) aφ = aρφρˆ + aφφφˆ + azφzˆ (D.56) az = aρzρˆ + aφzφˆ + azzzˆ (D.57) Differential operations dl = ρˆ dρ + φˆ ρ dφ + zˆ dz (D.58) dV = ρ dρ dφ dz (D.59) d Sρ = ρ dφ dz, (D.60) d Sφ = dρ dz, (D.61) d Sz = ρ dρ dφ (D.62) ∇ f = ρˆ ∂ f ∂ρ + φˆ 1 ρ ∂ f ∂φ + zˆ ∂ f ∂z (D.63) ∇ · F = 1 ρ ∂ ∂ρ ρFρ + 1 ρ ∂Fφ ∂φ + ∂Fz ∂z (D.64) ∇ × F = 1 ρ ρˆ ρφˆ zˆ ∂ ∂ρ ∂ ∂φ ∂ ∂z Fρ ρFφ Fz (D.65) ∇2 f = 1 ρ ∂ ∂ρ  ρ ∂ f ∂ρ  + 1 ρ2 ∂2 f ∂φ2 + ∂2 f ∂z2 (D.66) ∇2 F = ρˆ  ∇2Fρ − 2 ρ2 ∂Fφ ∂φ − Fρ ρ2  + φˆ  ∇2Fφ + 2 ρ2 ∂Fρ ∂φ − Fφ ρ2  + zˆ∇2Fz (D.67)