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John,
You seem to be solving a different problem. There's is an inertial
reference frame O in which the two spaceships, one in front of the
other, are initially at rest. There is a rope stretched from the tail
of the spaceship in front (point A) to the nose of the other spaceship
(point B). At time zero in that frame both spaceships start
accelerating.*/The way I read the problem, the spacecraft are stipulated
to accelerate in such a manner that the projected (onto frame O)
separation of point A and point B never changes. You have them/*
accelerating such that an accelerometer on the tail of the lead
spaceship always has the same reading as an accelerometer on the nose of
the trailing spacecraft. That's a different problem.