orbit - How to get the longitude of the perihelion to find the Heliocentric Equatorial coordinates of a planet

I'm writing a program to randomly generate star systems and I have been having a difficult time figuring this out. I've found the equations I need to get the heliocentric equatorial coordinates, but I haven't been able to figure out how to determine the longitude of perihelion. Is it just the opposite of the longitude of the ascending node or is it a completely different variable?

It might just me, but the names for this stuff is definitely making it more confusing than it should be.

Here is all my notes:

** = power

P = planet's period

a = semi-major axis

b = semi-minor axis

M = mean anomaly

E = Eccentric anomaly

e = eccentricity of orbit

v = true anomaly

r = radial distance

A = longitude of asending node

w = longitude of perihelion

i = inclination

t = time

(r, v) = polar coordinates

(x, y, z) = Heliocentric Ecliptic coordinates

(X, Y, Z) = Heliocentric Equalorial coordinates

eccentricity

e = sqrt(1 - (b ** 2 / a ** 2))

Period

P = sqrt(a ** 3)

Kepler's Equation

M = E - e * sin(E)

Mean Anomaly
use as starting point for eccentric anomaly

M = (2 * pi * t) / P

True Anomaly

v = 2 * atan(sqrt((1 + e) / (1 - e)) * tan(E / 2))

Radial Distance

r = (a(1 - e ** 2)) / (1 + e * cos(v))

Heliocentric Ecliptic coordinates

x = r(cos(A) * cos(w + v) - sin(A) * sin(w + v) * cos(i)

y = r(sin(A) * cos(w + v) + cos(A) * sin(w + v) * cos(i)

z = r * sin(w + v) * sin(i)

Heliocentric Equalorial coordinates

X = x

Y = y * cos(i) - z * sin(i)

Z = y * sin(i) + z * cos(i)