If input energy is unmetered then how could the sim solve to unity when a) braking is disabled, and the OB axis simply allowed to catch up with the rotors under its own OB torque, and b) when the spin cycles are omitted too?Fletcher wrote:FWIW, and while you contemplate your above questions and answers.
I suspect that in your V1 rig that some energy input is not being accounted for. Hope I'm wrong on that.
e.g. Your Actuators are length controlled. Usually an Actuator contracts or expands by applying a force over a distance (doing Work).
You might consider replacing the Actuators with either Separators or Rods which can also be length controlled by a bit of creative equationing I should think.
Do you still have the same gains ? If so, it might be that formula driven length changes are not accounted for in the sim energy budgets. IOW's they happen for free because they are length driven and the sim doesn't care where the energy comes from to change the length.
Maybe you already covered this discussion but thought it worth mentioning again, as a comparable test scenario to try and nail down where these gains are coming from.
ETA : it pays to have Integration Steps (Accuracy) on Variable as Wubbly discussed recently when using them as Catches and Latches etc.
The motor's input torque * angle is a constant function of the constant MoI's relative to the constant gravitational acceleration.. you can see it's the same energy under every impulse on the plot, and the net motor integral is simply that value times the number of blips..
Yet the gain only arises as a function of the motor work done.. and they're doing the right amount of work in the rotating FoR, while the resulting KE and CF-PE rises are proportionate in the static FoR; a 1 rad/s reactionless acceleration on a 1 kg-m² MoI already at 1 rad/s only costs half a Joule, yet causes a 1.5 J energy rise in the static frame.. this is the 'excess energy source', which is then being harvested by the solenoids in the form of CF-PE.
If this energy was instead being provided by the solenoids themselves, then that section of the curve plot would be positive - ie. remaining above the '0' line... yet we see that it quite causally and deliberately ventures down below the zero line, to then carve out this sizeable chunk of negative energy; ie. that lower bulge on the tail of the solenoid integral is work being done against the solenoids, by CF force, which itself is the internal expression of the rotKE gain caused by the momentum gains yielded from the reactionless s&b cycles sinking counter-momentum to gravity.
Input energy is being measured as the time integral of force * velocity * time - those 'P*t' meters - thus the force is being measured at every frame / integration step.
Actuators produce clean integrals, since they're being used as designed.
Using rods or separators instead produces completely unusable data - they're not intended to be used this way, and so this suggestion would render all measurements impossible while providing no functional benefits; at best, all you'd end up with is an animation, but it wouldn't be a 'sim' and couldn't produce data of any quality..
Variable integration steps should never be used for data acquisition - if ever - since it works kind of heuristically, paying more attention when say collisions are occurring, while 'smoothing over' / skipping more routine integration steps with basic assumptions; ie. providing a result that simply assumes prior integration steps would've proceeded or transpired as expected, without actually simming them all discretely..
So in Wubbly's example, the sim simply bypassed the complexities of actually modelling the specific details of the collision involving the 'catch' mechanism, and with it, any of the vagaries of the insufficient sim frequency / # of integration steps that were being used at the time.
That is to say he could've got the system working better chiefly by raising the frequency, with perhaps a little tuning of i-s/f too; generally 1 integration step per frame provides best baseline consistency, and too many i-s/f can itself produce juddery corrections between frames.
So there's no 'mystery' as to the provenance of the gains - the source, i've described a thousand times...
..the reactionless s&b cycs generate the energy gains from within the rotating FoR, relative to the static FoR..
..and the asymmetric inbound vs outbound radial velocities are harnessing those energy gains in the form of CF-PE.
The priority is simplifying the gap regulation mechanics to its bare fundaments; solving this will result in the potential to switch out the actuators for springs, harnessing that CF-PE gain directly as input GPE.
Anyone needing a refresher on how and why reactionless s&b cycles / successively sinking counter-momenta to gravity is an inherently-OU process should study the original 'chicken run' demo, included in post#1.
Anyone stuck on as to why the gain has to be collected in the form of CF-PE needs to meditate on the fact that any RPM increase on a GPE cycle - whatever its provenance - necessarily causes the rate of input GPE to increase per unit time, and thus the rate of GKE output along with it, thus it is clearly mathematically impossible to ever decouple GPE from rotKE! That would effectively be invoking a GPE asymmetry, any notion of which can only be a barrier to progress. Hence any rotKE gained from onboard asymmetric inertial interactions must - and can only be - harnessed in the form of CF-PE. Obviously it is then immediately available to assist in the radial lifts powering the OB cycle.
Anyone still itching for deeper insights will probably find 'em in the sims and measurements already provided - again, that pink line integral has a net area below the '0' line, and that greater area, relative to that enclosed above the center line, is the energy gain / discounted PE.
