Parabolic Cylindrical Coordinates - Printable Version +- 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