Please pardon my being dense. I don't mean to cause any upset but I am having a problem trying to synthesize concepts. I can't put all the concepts of this 'return to center thing' into something that makes sense to me.
A return to center force is the defining force for oscillation. Think spings without shocks. You do not want back and forth sway any more than you want your truck to act like a bouncy baby buggy.
I am confused about the cause of the force: "Reversal of this lateral acceleration is part of the normal oscillatory behavior." I do not see oscillation as normal behavior nor do I think the source of the "lateral acceleration" that would cause such behavior is very clear.
Another issue is the confusion between a self centering force and the straight rig objective. Adding rigidity to the rig articulation ability would only change the frequency. The way to eliminate oscillation is to dampen the movement like shock absorbers do.
What really gets interesting to me in this conundrum is the stability consideration. Catastrophic 'oscillating' sway that seems to be the big concern is not a stable situation. It starts minor and builds. This is not your typical oscillating system which is a slightly perturbed stable system trying to return to its steady state. To build an oscillation you have to add energy at just the right times, enough to overcome damping forces and friction. How is this done in a trailer 'oscillating' sway disaster?
I do know that there are unstable rigs. Driviers figure this out right away as the lack of stability becomes obvious as speed increases and they usually stop and fix the problem before it causes loss of control.
Then there is the handling comfort involving driver fatigue going down the road. The rig needs constant attention as it is very responsive to even minor stimuli on the road.
Then there is the dreaded catastrophic oscillating sway. This is usually due to an inability to control a maneauver. Most common are downhill and/or hard braking turns followed by, perhaps, response to unexpected winds and gusts. The energy input here is obviously kinetic and the control mechanism is the driver.
I guess the big question is how all these considerations help move towards safer towing. In my mind, it is a good idea not to be too confident in what one thinks one knows. On this topic, it may be that confidence in knowledge is a bit out of line with the quality of that knowledge. And knowing that may encourage safer driving.