2. All the softball data I have seen support the notion that the trajectories are smooth and the movement is continuous. That is even true of most (but not all) of the knuckleball trajectories I have analyzed. Keep in mind once again that I am talking about real data that use either video or radar tracking to give the position of the ball as it moves along its trajectory. Hard to argue with real data.
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One big thing that I could not discern from your website was what you mean by smooth as it relates to curvature. For instance, both the curvature of a circle and a parabola are "smooth" but one is constant and the other changes with position. As we have discussed late break here, I think there are basically two positions, the first is that the curvature is a constant arc as it would be on a circle and the other is that the curvature changes as it would be on a parabola. I think the circular people are the "no late break" folks. The parabolic folks (late breakers-including your truly) think that while it is still "smooth" that the majority of the break on a good breaking pitch is further along in the travel. Set us straight.
the other thing I am really curious about is whether, based on your research, can a knuckleball break in more than one direction in a single pitch (hint-say yes so I don't have to eat humble pie).
Both of these are good questions. Regarding circle vs. parabola. A parabola results if both the magnitude and direction of the force is constant (example: gravity). A circle results if the magnitude is constant but the direction is always perpendicular to the velocity. Over a short enought distance, the two types of trajectories are pretty indistinguishable. And, as you point out, both are smooth. And in both cases, the break is continuous. The PITCHf/x data from MLB (many 1000's of pitches) cannot easily distinguish the two possibilities (the radius of curvature of the circle is very large). Here is a link to the article I wrote a while abo about late break: Baseball Prospectus | BP Unfiltered: Is "Late Break" Real?. If you look at the trajectory, you see that the amount of deflection is greater during the last half of the trajectory than in the first half. That's just a mathematical property of circles/parabolas. In that sense, the break is late. But it is continuous.
Regarding your k-ball question, multiple breaks are possible, albeit not all that common (at least among the hundreds of pitches I have analyzed). Here is a great example and my explanation of it: Dickey's Nasty Knuckleball.