This looks very interesting, the problem has been essentially solved. Can you send over the lagrangian used for this solution? It will be very interesting. The result is right, the nutations and precessions are very slow compared with the orbital interval. Congratulations on this solution!
Sent: 12/02/2017 19:36:52 GMT Standard Time
Subj: dumbbell orbit
I plotted the orbit of the centre of the dumbbell (blue) and one mass of
the dumbbell (red). It can be seen that the centre of mass moves on a
plane elliptic orbit. The dumbbell shows nutation and precession. This
is the most simple model without a rigid body, requiring two mass points
with constraints. These mass points represent a ring which gives the
same Lagrange equations. This may also be a method for computing the
Milankovitch cycles where the parameters are different:
nutation/precession is very slow compared to the elliptic orbit.