3 ms·

Hmmm. Is there really a fold though? If you added velocity and position above the water into the mix then the state transition is unique and smooth. The fold ap

Hmmm. Is there really a fold though? If you added velocity and position above the water into the mix then the state transition is unique and smooth. The fold appears because important quantities are not plotted and resolved elsewhere. The only real discontinuity is the when the hull touches the water. Maybe I don't really know the definition of a catastrophe. To me a PID controllor exhibiting ringing would look "folded" in position space (smooth in position/velocity space).

ColinWright 13y ago
If you plot "Steady State Driving Force" against "Steady Speed" then for any given craft there is a curve. This curve the changes from simple quadratic(ish) through to the version discussed for the hydrofoil. We can think of this as adding every more efficient and effective foils to a more-or-less standard craft. Now in the space "Foil Size" x "Driving Force" we plot "Resultant Speed" and we get a classic folded manifold, including the singularity. So yes, there really is a fold. Physics tells us that if you include lots and lots of things in your phase space then all the transitions are "smooth." Even here, when the craft touches the water and decelerates dramatically, almost "catastrophically", the transition (when considered in sufficient detail) is smooth. We can plot keel height above water, and as that gets to -1 mm then the deceleration is increasing smoothly, etc. However, dealing with this on a macro level, it's more useful to consider the dynamics as being a fold catastrophe.