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I also hope to learn more from John's simulation, and from its
interpretation. But for the time being I do not see why the
"synchronization without friction" would automatically violate
classical physics.
I did not get rid of any angular momentum. Neither Earth nor Moon
were given spin at time zero (in the frame of reference of the
center of mass). Moon starts spinning (tries to show us the same
face). I assume this is at the expense of the orbital angular
momentum. But this has to be checked; all sort of speedometers
are available in IP. I watched the system for only two ratations.
Some interesting oscillations (of the double-moon's axis with
respect to the line between the centers of E and M) were quite
obvious. I wish I had more time to play with this system.