Python billiards collision response some angle problems with my formula

Question

This is my collision response code for a billiards simulation of 2 moving balls colliding. I used newton's laws of equation and then parametrised the components of the velocity vectors,

Alpha is the trajectory of ball 1
Beta is the trajectory of ball 2
Theta is the angle of the line of centres with respect to the axis

My idea was to come up with a general formula for collision response in the local frame of the 2 balls then reproject it back into my fixed frame, but I noticed that there are some angle problems, I can't figure out for my life what conditions should be for i.e. alpha

the last bit is just to make sure the balls aren't overlapping after the collision and get stuck in an infinite loop of colliding

    def collision(b1,b2):

        dx=b1.x-b2.x
        dy=b1.y-b2.y
        Theta = atan2(dy,dx)
        Vx1=b1.speedx
        Vy1=b1.speedy


        Vx2=b2.speedx
        Vy2=b2.speedy

        V1 = sqrt((Vx1)**2+(Vx1)**2)
        V2 = sqrt((Vx2)**2+(Vx1)**2)
        Alpha = asin(Vx1/V1)
        Beta = asin(Vx2/V2)


       b1.speedx = (((1-e)/2)*V1*sin(Alpha-Theta) - ((1+e)/2)*V2*sin(Beta-Theta))*sin(Theta) - V1*cos(Alpha-Theta)*cos(Theta)
       b1.speedy = (((1-e)/2)*V1*sin(Alpha-Theta) - ((1+e)/2)*V2*sin(Beta-Theta))*cos(Theta) + V1*cos(Alpha-Theta)*sin(Theta)
       b2.speedx = (((1+e)/2)*V1*sin(Alpha-Theta) - ((1-e)/2)*V2*sin(Beta-Theta))*sin(Theta) + V2*cos(Beta-Theta)*cos(Theta)
       b2.speedy = (((1+e)/2)*V1*sin(Alpha-Theta) - ((1-e)/2)*V2*sin(Beta-Theta))*cos(Theta) - V2*cos(Beta-Theta)*sin(Theta)

Answer 1

Don't use asin to compute the angle. If you insist in using angles (instead of vectors) you should use atan2.