Hi Gents,
I'm trying to write something to go from kepler parameters to a position and
velocity vector.
This article was a great help
http://www.ucalgary.ca/~sneeuw/lectu...423/kepler.pdf

But I can only get orbits that look real (ie: the Earth is in the correct
place) if I change the sign of the rotations, specifically, change the line
r = R3(-Om)R1(-I)R3(-w)q

into

r = R3(Om)R1(I)R3(i)q

and same for velocity. Then all my planets end up in the right 'place'.

When going back from velocity to position, I again need the sign change, but
I'm having unrelated problems with totally circular orbits.
Obtaining a (semi-major azis) and e (eccentricity) from the position and
velocity vector is easy enough, but if e is zero, then I do not know how to
calculate the eccentric anomaly (E).
An equation is given for distance a body at a distance r
Cos E = (a-r)/(a*e)
As you can see, for circular orbits this is undefined.

I realise that in the circular orbit case the eccentric anomaly is equal to
the mean anomaly, but the above paper calculates the mean anomaly from the
eccentric anomaly! Simply obtaining the angle in the q-plane doesn't work
either, because one of the rotations to create the q-plane is created from
the Eccentric anomaly!
But I waffle on...How can I calculate the eccentric anomaly for circular
orbits?