jim,
thanks for replying.
i must, at the current state of my knowledge, ultimately admit ignorance as to what is actually going on with respect to physics. from reading your other posts on this thread, perhaps you can shed some light. (i would be interested in seeing the equations you came up with from your earlier post.) i am mainly going on observations on the table combined with some, albeit weak, heuristic arguments, and could very well be wrong.
first, let's agree that a rolling ball means that it travels one circumference when it rotates along the horizontal axis (i.e. forward spin) once. if it travels more than one circumference when it rotates once, then it's "under spinning." if it travels less, it's "over spinning." when it's rolling, as opposed to under or over spinning, it's grabing the cloth more, i think. this is admitedly vague; perhaps you can state it more precisely. it's this grabbing that, if true, is causing any side spin to dissipate more quickly. there are other effects of a rolling ball that go unnoticed by many players (i think), which may add some insights to this.
for instance when a cue ball is rolling when it hits an object ball with, say, a half ball hit, it will follow earlier than if it's over spinning. that is, an over spinning ball will travel along the tangent line (or close to it) longer than a rolling ball, before it follows forward. most people, i believe, think that it's speed alone that determines this, but i think whether it's rolling or over spinning has more to do with it. note that a ball can be either rolling or over spinning at many different speeds. it starts to move forward when the speed and forward spin match, so to speak. when it "fully grabs," it's matched.
i hope you can add some further insight and analysis to this, whether i'm right or wrong.
william