State vectors of "interesting" multiple stars I'd like to show a demonstration of Runge Kutta integration of real systems using examples of interesting multiple stars, where "interesting" means you can see through a small telescope that they are at least double. I've selected three:


Gamma Andromedae (Almach)
Alpha Geminorum (Castor)
Zeta Ursae Majoris (Mizar and Alcor)


How can I find a state vector (set of relative positions and velocities) - or something similar - for these multiple star systems? An open access link (for everyone) would be great, but a journal reference is fine as well if that's what it takes.

Of course the periods are long and there will be uncertainty - I'd just like to use whatever is known and available, for this demonstration.
The USNO Sixth Catalog of Orbits of Visual Binary Stars (ORB6)
has the orbital elements you need.


$\gamma$ And is WDS 02039+4220
$\alpha$ Gem is WDS 07346+3153
$\zeta$ UMa is WDS 13239+5456


Double star expert Bruce MacEvoy explains orbital elements in maybe enough detail to help you work out some state vectors.
My search also turned up a book chapter by Andreas Alzner.