There is definitely some ambiguity in what is meant by "a player is required to come to a stop", as this comes up frequently.
The answer has some grey in it, and this is a case where I think there should be a change to the rule for more clarity.
The issue comes down to what does "stop" mean. When a pivot is set, the foot is stopped. However a player is almost never truly motionless when they have the disc. Obviously a player is not expected to become a statue, so there is some amount of movement allowed while still meeting the criteria of "stopped".
Obviously the way ultimate is intended to be played is with a certain amount of flow. Nowhere is anybody suggesting that players have to stand upright and motionless for a beat before every throw, though this could be interpreted from the rule.
Further, the rules (II.M) support establishing a pivot while not being stopped.
I interpret the rule the following way:
1) If a players slowing movement results in them being *able* to retain contact with their pivot point indefinitely, then they are considered to be stopped once that pivot touches the ground, regardless of whether their upper body is moving about that pivot. Any throw made while that pivot point was established is not a Travel. This remains true, even if the thrower chooses (but was not forced by his momentum) to move that pivot point after the throw is released.
2) If a player throws a disc and they would not be able to retain the pivot after the throw, then they are not stopped, and it is a travel.
Like I said there's some gray area there, and the rule should be changed. I've been trying to think of a change to the rule that would explicitly allow 1) while still disallowing 2), but I'm still working on it.
Craig