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Expressing Spherical coordinates in terms of cylindrical

  • Thread starter armolinasf
  • Start date
  • #1
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Homework Statement


I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help!



The Attempt at a Solution



Spherical(cylindrical)

r=(ρ^2+z^2)^(1/2)
θ=arcsin(ρ/(ρ^2+z^2)^(1/2))
ψ=ψ

Cylindrical(Spherical)

ρ=rsinθ
z=rcosθ
ψ=ψ
 

Answers and Replies

  • #2
19,672
3,983

Homework Statement


I'm trying to express spherical coordinates in terms of cylindrical and vice versa. I would appreciate it if someone could give me some feedback on my attempt at a solution. Thanks for the help!



The Attempt at a Solution



Spherical(cylindrical)

r=(ρ^2+z^2)^(1/2)
θ=arcsin(ρ/(ρ^2+z^2)^(1/2))
ψ=ψ

Cylindrical(Spherical)

ρ=rsinθ
z=rcosθ
ψ=ψ
What you've done is already correct. What more are you asking? Incidentally, you might want to use θ=arctan(ρ/z) instead of θ=arcsin(ρ/(ρ^2+z^2)^(1/2)), but that is a matter of taste.
 

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