Regarding friction circle, just in case someone needs it outside of the code. The math is following:
if we take a parametric ellipse equation
x = a * cos(t)
y = b * sin(t)
[where t=0…2Pi]
then our muX and muY (friction coefficients in X and Y axis of the wheel) can be used as radius of ellipse
x = muX * cos(t)
y = muY * sin(t)
we can find t from a dot product of relative velocity vector of the wheel and forward vector of the wheel
t = arccos( dot(V, Fvector))
substituting we get
x = muX * dot(V, Fvector)
y = muY * sqrt(1 - dot(V, Fvector)^2 )
then final friction coefficient mu is just length of the vector (x,y), which is a point on the ellipse in the direction of velocity
mu = length(x,y)