Prime 6 sheet in attach.
I think you essentially have not a three- but a two-bodies problem, since m1 and m2 cannot move freely with respect to each other.
Yes! We can say - it is a two-bodies problem or a three-bodies problem with one (pseudo) hard link!
See please the attach - Prime 6 and Mathcad 15
There is no general closed-form solution to the three-body problem, meaning there is no general solution that can be expressed in terms of a finite number of standard mathematical operations. Moreover, the motion of three bodies is generally non-repeating, except in special cases.
You are replying to a SPAM posting, the message text was copied from here: https://en.wikipedia.org/wiki/Three-body_problem#General_solution
We are experiencing that kind of annoying spam quite often here in this forum (and also in others). Usually a link is added (the main reason for the post) which probably was already removed by a moderator. Because the message text looks appropriate at first sight, the mods obviously are not sure if its vital to the thread or not and so they unfortunately hesitate to remove the whole posting.
A clever way for a spam post, but quite annoying to us.
I also noted sometimes, that the initial post does not contain the link but its rather added only later (when the post had already passed moderation). Quite sophisticated and hard to deal with.