Start with small e and beta=1, then try increasing beta, e etc 
one parameter at a time. Try different values of beta for 
 fractional values of eccentircity and animate angle phi
for each value of beta. The parameters can be changed using the sliders.
Click on the screen and drag a bit to refresh display.

β = 1 (slider from 0.5 to 4, step 0.1)
r0 = 1 (slider from 0 to 3, step 0.1)
e = 0 (slider from 0 to 1.2, step 0.005)
phi = 68.24997 (slider from 0 to 2000, step 1.0E-5)
radial: r0 / (1 - (e * cos((β * phi / 50))))
A: (radial; phi / 50)