Special treatment at coordinate origin, wrong! to be deleted

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13.3 Special treatment at coordinate origin, wrong! to be deleted

Ψ ≈ a00 + a10R + a01Z + a11RZ + a20R2 + a02Z2.

(407)

∘ -- R = R0 + b11 ψ cos𝜃

(408)

-- Z = Z0 + c11∘ ψ sin 𝜃

(409)

( ∘ -- ) ∘ -- ( ∘ -- ) ∘ -- ( ∘ -- )2 ( ∘ -- )2 Ψ ≈ a00 + a10 R0 + b11 ψcos𝜃 + a01c11 ψsin 𝜃+ a11 R0 + b11 ψ cos𝜃 c11 ψ sin 𝜃+ a20 R0 + b11 ψ cos𝜃 + a02 c11 ψ sin𝜃 ∘ -- ∘ -- ∘-- ∘ -- ∘ -- ∘ -- = a00 + a10R0 + a10b11 ψcos𝜃 + a01c11 ψsin 𝜃+ a11R0c11 ψ sin 𝜃+ 1a11b11 ψc11 ψ sin2𝜃 +2a20R20 + a20(b11)2ψ cos2𝜃 + 2a20R0b11 ψ cos𝜃 + a02(c11)2ψ sin2𝜃 ∘ -- ∘ -- 2 = d0 + d1 ψcos𝜃+ d2 ψ sin𝜃 + d3ψsin 2𝜃+ d4ψ cos2𝜃 + d5ψ sin2 𝜃

Ψ = d₀ + d₁

cos𝜃 + d₂

sin𝜃

R = R +b11∘ ψcos𝜃 + b12∘ ψ-cos2𝜃 + b21( ∘ψ-)2cos𝜃+ b22(∘ ψ)2 cos2𝜃 0

(410)

( ) ( ) Z = Z + c11∘ ψ-sin𝜃 + c12∘ ψ-sin2𝜃 + c21 ∘ ψ- 2sin 𝜃+ c22 ∘ ψ-2sin2𝜃 0

(411)

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