When you say they end up not in the right place, are
you referring to a screen plot of the position

The correct place in space. I have tables which say where Earth and Mars
should be. I can only get them there by reversing the sign of the rotations.
It probably is an axis problem, though I cannot see what. My axes are very
consistant. But I am wondering if the author of the paper I mentioned
previously made an error.

Exactly which parameters are you given to start with
for your circular orbit?

Semi major axis, eccentricity, inclination, longitude of ascending node,
longitude of perihelion, mean longitude [at epoch].

The classical orbit elements
can be tricky to work with in specific cases. For example,
for an equatorial orbit Om, the longitude of the ascending
node is undefined. For a circular orbit, the argument of
periapsis and the true anomaly (along with the mean and
eccentric anomaly) are undefined, since there is no
periapsis.

So for an equitorial, circular orbit I lose 3 parameters?
How can the true anomaly be undefined? The body must lie at some point on
the orbit at a given time.

In these cases you have to work from the
longitude of the ascending node. Perhaps the argument of
latitude at epoch will be given (angle between ascending
node and the position vector at epoch)?

The argument of latitude at epoch can be calculated (ref the paper), but
depends on Om.