Parabolic Cylindrical Coordinates
03-05-2017, 03:02 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 936 Joined: Dec 2013
Parabolic Cylindrical Coordinates
Parabolic Cylindrical Coordinates

The relationship and conversion factors between parabolic cylindrical coordinates (μ, v, ϕ) and rectangular coordinates (x, y, z) are as follows:

x = 1/2 * (μ^2 – v^2)
y = μ * v
z = z

μ = √(x + √(x^2 + y^2))
v = y / μ
z = z
(note the sequence)

where μ ≥ 0

HP Prime Program PCC2REC (Parabolic Cylindrical to Rectangular)

Code:
EXPORT PCC2REC(μ,v,z) BEGIN // 2017-02-27 EWS // Parabolic Cylindrical // to Rectangular // μ≥0 LOCAL x:=1/2*(μ^2-v^2); LOCAL y:=μ*v; RETURN {x,y,z}; END;

HP Prime Program REC2PBC (Rectangular to Parabolic Cylindrical)

Code:
EXPORT REC2PCC(x,y,z) BEGIN // 2017-02-27 EWS // Rectangular to // Parabolic Cylindrical // μ≥0 LOCAL μ:=√(x+√(x^2+y^2)); LOCAL v:=y/μ; RETURN {μ,v,z}; END;

Example

μ = 2, v = 3, z = 1
Result: x = -2.5, y = 6, z = 1

Source:
P. Moon and D.E. Spencer. Field Theory Handbook: Including Coordinate Systems Differential Equations and Their Solutions. 2nd ed. Springer-Verlag: Berlin, Heidelberg, New York. 1971. ISBN 0-387-02732-7
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