Math Overflow must be one of the most extreme examples of successful communication on a narrow topic between people at widely different levels of fame/skill.
However, I'm left a little confused at the end, by this:
> The process then repeats itself (imagine a marble rolling frictionlessly between two equally tall hills, starting from a position very close to the peak of one of the hills).
But it's not really just two hills, I think. It must be two hills in a closed space, because you can get from one peak to the other in either direction. Yes?
Also, back in physical reality, I wonder whether the periodic axis rotation continues in the same direction, once a small perturbation gets it started. Or whether the direction of axis rotation randomly changes. Anyone know?
When I saw this thread, I was sure that it would be something about orbital mechanics or the Coriolis effect. But no, it seems.
* For each M-mass, the centrifugal-vector lies along the x-axis.
* For each m-mass, the centrifugal-vector lies along the z-axis.
* For each centrifugal-vector, the magnitude is proportional to "the point-mass's distance from the disk's axis-of-rotation (the y-axis)". Since the m-masses move along a unit circle in the yz-plane, their magnitudes vary.
E.g. an m-mass which starts at (0, .9, .1) will accelerate towards (0, 0, 1) then deccelerate towards (0, -.9, .1). Then it will retrace its path. This results in oscillation between (0, .9, .1) and (0, -.9, .1) along a semi-circle in the yz-plane.
N.b. no oscillation will occur if an m-mass starts at exactly (0, 1, 0).