+- HP Forums (https://www.hpmuseum.org/forum)
+-- Forum: HP Software Libraries (/forum-10.html)
+--- Forum: HP Prime Software Library (/forum-15.html)
+--- Thread: Parabolic Cylindrical Coordinates (/thread-7870.html)
Parabolic Cylindrical Coordinates - Eddie W. Shore - 03-05-2017 03:02 PM
Parabolic Cylindrical Coordinates
Link: http://edspi31415.blogspot.com/2017/03/hp-prime-parabolic-cylindrical.html
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