I got completely confused reading VRBones post of Nov 6, 6:01pm (6:25 edit) because I could not make heads or tails of the various additional forces, steps, cycles, and waves. However, I managed to think about it on my own, and even uncovered another error that ocurred to me in my talk with baggio.

I found that the final energy dissipated by the system does not stay equal with any gravity ramp (as I erroneously stated), but potentially decreases as the number of steps is increased.

I found this out by first looking at a vertical bar fixed at one end, without damping applied; if you go to 0.5 g and then take it to 1g as the oscillation is at its lower extremity, it will come to rest immediately; if you do that step at the upper end of the oscillation, you might as well not have bothered with 0.5 g.

Also note that at static equilibrium point, internal energy is equal to kinetic energy; it is half the work done by gravity (m*g*y, y being the displacement downwards) because internal beam force starts at 0 and is m*g only at equilibrium.

Now think of that same bar; at final g, let it's gravitational force be G, with an equilibrium displacement of y. Ramping up g in n steps and assuming we let the structure reach equilibrium between the steps gives us the work Wi per step i as displacement per step (y/n) * strength of gravity force at that step (i/n)*G :

Wi = (y/n) * (i/n)*G

Summing up Wi for i=1 to n gives us total work done:

W = G*y/2 + G*y/(2*n)

The first term G*y/2 is equal to the internal beam energy at equilibrium; the second term is equal to the excess energy that must be damped away. This energy decreases in inverse proportion to n.

However, this result is at best an average value when the system is not at rest between the steps.

What we do not know is how damping is affected by this; I still fear that such a procedure might increase the time the structure needs to settle, and the right timing for the steps has not been determined, either (and might vary with the structure, so might have to be dynamically computed).

In hindsight, VRBones first paragraph now makes some sort of sense to me; paragraphs 2 and 3 still leave me stranded.