Re: [seekfun] Good save, sir.
I have also experienced the pendulum effect that try2live described.
I don't think it's about forces through the "hinge point," I think it's better visualized as where the jumper's center of mass is compared to the aerodynamic center of the wing. When you push off and do a short/no delay, and have an on-heading, you are in front of your canopy's direction of travel, and you swing backwards relative to the wing. It happens so fast you might not notice it. But open in a full track and you can't ignore it.
If you had a 180 on this same jump, you are now aft relative to the canopy's direction of travel, and you will still swing back under the canopy. Which is "backward" from your point of view, because you are facing the trailing edge of the canopy. But the canopy is facing the other direction, so it surges "forward" in that direction as you spin out of the 180-- hence the forward surge.
A more technical explanation:
Every wing has an inherent pitching moment, which is the difference between the center of pressure and the aerodynamic center of the wing. In an airplane, this moment is counterbalanced by the horizontal stabilizer and elevator inputs.
A parachute does not have an empennage, so the pitching moment is counteracted by where underneath the canopy the jumper is hanging, and it can be a very sensitive position (i.e. just put a tiny bit of pressure on your front or rear risers). In the first instant after opening, the moment caused by the hanging jumper is not yet in equilibrium with the pitching moment, hence a pendulum swing until equilibrium is established. It's an inherently stable system that is well-damped and quickly reaches equilibrium.
Furthermore, although it's perhaps more subtle:
If you have line twists, and not just a simple 180 half twist, the "hinge point" as you call it shifts upward. Additionally, and someone correct me if I'm wrong, but line twists will shorten different line groups unequally. I can remember line twists where one riser's lines were shortened subtly more than others, and the result is canopy warp, and an induced turn until the twists are cleared.
And even with just a simple 180, still think about what it is doing to the effective canopy trim. There is probably some effect and depending on how asymmetric the twist is, could be very noticeable.