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11.42: A.6.4- Section 6.4 Answers

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1. If e=1, then Y2=ρ(ρ2X); if e1(X+eρ1e2)2+Y21e2=ρ2(1e2)2 if; e<1 let X0=eρ1e2,a=ρ1e2,b=ρ1e2

2. Let h=r20θ0; then ρ=h2k,e=[(ρr01)2+(ρr0h)2]1/2. If e=0, then θ0 is undefined, but also irrelevant if e0 then ϕ=θ0α, where πα<πcosα=1e(ρr01) and sinα=pr0eh.

3.

  1. e=γ2γ1γ1+γ2
  2. r0=Rγ1,r0=0, θ0 arbitrary, θ0=[2gγ2Rγ31(γ1+γ2)]1/2

4. f(r)=mh2(6cr4+1r3)

5. f(r)=mh2(γ2+1)r3

6.

  1. d2udθ2+(1kh2)u=0,u(θ0)=1r0,du(θ0)dθ=r0h
  2. with γ=|1kh2|1/2
    1. r=r0(coshγ(θθ0)r0r0γhsinhγ(θθ0))1
    2. r=r0(1r0r0h(θθ0))1
    3. r=r0(cosγ(θθ0)r0r0γhsinγ(θθ0))1

This page titled 11.42: A.6.4- Section 6.4 Answers is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by William F. Trench.

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