Into the Vanishing Point..

[MrVibrating]

Just noticed a striking symmetry in the 10:1 plot - at precisely 1 meter radius, both masses have exactly the same momentum, a 50/50 split, but with a 1:10 KE split:



I thought it probably worthwhile tabling up the whole interaction, as yet another interesting symmetry seems to be implied:



..the sim craps out 14 mm from the center, but it looks as though, were it able to make it all the way in, we'd end with precisely the same amount of momentum we began with - so in essence, gradually pulling the 10 kg mass inwards causes the net system momentum to more than double, then subside back to its starting level.. even as KE continues rising unabated.

The energy value of the remaining momentum thus hits ~28 times its nominal value..

As for the negative cost of momentum in the final 2 meters, read it as positive cost of negative momentum, ie. "3.451 Joules per negative kg-m/s". Adding energy here is reducing momentum, instead of increasing it.

Apparently, anyway. That's what the hypothesis predicted, and the sim seems to be concurring...

[MrVibrating]

...presumably these momentum change costs correspond to accelerations of the system center of mass - i can tweak the sim to highlight this...

..so if it's the system center of mass that's decelerating over the final 2 meters, these figures should square with the KE=1/2mV^2 rate.

This is a new angle for me at least - considering the momentum and KE properties not of the masses, but of the empty space between them, and its 'motion'... of space, through space.. it's as incongruous as it is logical...

[MrVibrating]

Raising the integrator accuracy to billionths gets the radius down to virtually zero:




...as i'd thought, then, net momentum is conserved at the end of the interaction... despite more than doubling during it.

Energy has been raised eleven-fold from 6 J to 66 J, RPM has risen from 1 to 11, and we have exactly the same amount of rest mass and momentum we started with.

This again suggests tantalising possibilities for the reverse interaction - can we likewise tap off 60 J without tapping off any momentum? This would potentially answer the conundrum as to how Bessler's wheels acheived the same feat: as i've pointed out, usually, you can't harvest raw KE without also harvesting momentum, so energy gains alone don't seem sufficient to explain his wheel's performance. An endless reservoir of fresh momentum to replace that being drained off with the output RKE would thus seem to be implied. An N3 break could supply that, in principle... if it were possible.

But if, OTOH, we can reduce this system's RKE 11-fold and yet end with exactly the same amount of momentum we began with, then no N3-break is required in the first place!

RKE and angular momentum would thus be decoupled, to some extent - we could change one without changing the other! That's what we appear to have done here, anyway...

Can hardly wait to start the reverse tests, winding the mass back out at 1 mm/s...

[MrVibrating]

So we have a really intriguing question here - where did that transient net momentum increase come from, and go to, before the sliding mass made it into the center?

We can answer that definitively, insofar as circumference and thus 'edge speed' increases with radius, and RPM's couldn't drop fast enough to keep momentum constant because of the 1 kg inertia that remained out at fixed radius.

So it was a time-dependent transient rise in momentum! Did we just "borrow momentum from time"?

Likewise, the introduced momentum had to disappear again, as no matter the RPM, orbital distance goes to zero when orbit itself does, and at dead-center the mass can have no orbital momentum.. It disappeared into ever-decreasing circles of vanishing space... traveling progressively ever-less distance per unit time / RPM.

The momentum rise was real, though - and it more than doubled in an otherwise-closed system...

Will it do the same when the mass is wound back out instead..? Maybe net momentum will drop, instead, or just remain constant since we're no longer inputting energy? I honestly don't know what to expect..

But here at least, angular momentum's 'conserved' at the end of the day... It's basically fully conserved, apart from the bit where it wasn't. But apart from that transient doubling of momentum, in a closed system, CoAM did a sterling job.

Still, can't help wondering - what if we'd harvested that transient gain by colliding it with something else?

[Tarsier79]

You can get involved in soms as much as you want. I umderstand how useful they can be. Build a real world model and compare. Sometes the difference is to large to ignore.

[ME]

So we have a really intriguing question here - where did that transient net momentum increase come from, and go to, before the sliding mass made it into the center?

Split your momentum into a radial and an angular component.

[MrVibrating]

OK been putting this off long enough, spent all day at work trying to decide what was going to happen, and still pretty much expecting that the reverse test will mirror the above results, but still doubting it'd pan out for one reason or another...

Entropy increases, and all that..

The thing is, as the 10 kg mass moves out of the center and starts to regain orbital angular momentum, this is obviously gonna brake the system - it's a negative torque, it's inertia, slowing the system down as it winds outwards. Per CoAM. So net momentum should decrease, right?

Except, that 1 kg mass at 10 m radius and 11 RPM doesn't want to slow down. So the 10 kg mass isn't free to do its thing, there's an inter-reaction going on... and so it actually gains momentum on the way out...

Now, if the angular momentum being gained by the 10 kg mass leaving the center, is all lost by the 1 kg mass out at full radius, then net momentum would remain constant.

But, remember, that's not what happened on the way in...

IOW, if the 10 kg mass, heading back out from the center, somehow gains more momentum than the 1 kg mass ever had in the first place, then it can't be the source of that angular momentum! IOW this couldn't be a simple "transfer" of momentum from one body to another - but more akin to induction, 'from' somewhere else...

And this is exactly what appears to happen here.. not only does the 10 kg mass gain more momentum than the 1 kg mass had to donate (~7 kg-m/s, so no small margin), but as a result, the net system momentum is not constant:





...i've compressed the X-axis to make room for the inverse traces but what you're seeing is the exact same curves from above, in mirror symmetry...


And so in consequence, we have a very simple, yet surprising conclusion from a very simple experiment:

- I began my previous "flippin' flywheels" thread with the notion of converting CF PE into more momentum, and so applying CoAM to raise the net system momentum in an otherwise closed system..

- The results here demonstrate that every single thing i tried to accomplish to that end was utterly redundant; all the guff with contra-rotating flywheels, rack and pinion etc., all of that was just excruciatingly dumb...

- To convert CF PE into fresh momentum, you don't need to attach anything to the sliding masses - just slide them out, and provided there's any other mass rotating at fixed radius, net momentum will increase!

Slide an orbiting mass outwards, while some other orbiting mass doesn't slide outwards... and we create momentum. For a little while, anyway. Slide in or out too far and it disappears again. Blink and you could miss it.

But net momentum can be increased. or reduced, it seems.. and without necessarily applying an equal opposite momentum elsewhere.. in principle, it appears we can more than double the momentum of a swung, radially-extending mass... just by letting it extend under CF, while another attached mass does not.

Logically, if this more than doubles the momentum, then an elastic collision will absorb half of that, still leaving more momentum than we had before the radial excursion..

IOW it would seem remiss of us not to try and harness this transient rise in momentum..

[MrVibrating]

You can get involved in soms as much as you want. I umderstand how useful they can be. Build a real world model and compare. Sometes the difference is to large to ignore.

What sent me down this route was a simple consideration of where orbital momentum goes when orbit decays, and the de-orbiting mass is free to rotate, or not, about its own axis?

So suppose you have an orbiting mass, which itself has perfect axial bearings; applying orbital angular momentum does not thus introduce axial angular momentum - if we marked the mass with a pen we'd see it was holding its axial orientation regardless of the orbital torques. We could spin it around our heads on the end of a rope, and if it began pointing north then it'd always be pointing north, because there's no axial torques acting on it.

Perfect bearings are unnecessary just to get a handle on the conceptual problem though - as orbital radius converges down to zero, the amount of space the mass is traveling and accelerating through per revolution is decreasing.

So no matter the RPM, if we draw a radially-sliding mass inwards towards the center far enough, then beyond some threshold proximity from the center - here around 2 meters - we start to decelerate it, losing angular momentum, along with the disappearing space and thus velocity per cycle.

So when it finally makes it into the center, it has no spin momentum either.

However, i've tried it using a square slot joint, and so forcing the radially-sliding mass to rotate along with its orbit, a la 'tidally locked', with no substantive change in outcome...

So the bottom line seems to be that orbital angular momentum comes and goes along with orbit itself..

It's a mathematical convergence.. and the sim only seems to confirm this, inevitably crashing out at some non-zero radius owing to the infinities and infinitesimals this causes..

But yes, a model is most certainly called for, if any of this pans out.. still very early in proceedings though, nobody should be trying to build anything right now, i don't want to be wasting time with any cargo cult engineering projects. Right now it's all so much abstract maths, and should stay this way until someone has a concrete design for a testing regime.

Testing the most recent prediction, for example, would require the following kind of rig:

- a small mass at fixed radius

- a big mass with a variable radius

- a means to measure speed

- ideally a rotor or radial / diametric pole / beam etc. with minimal mass itself (so that the other two masses constitute as much as possible of the total system mass)

..and that's all.

But hopefully we'll come up with something slightly more compelling before stalling for too long on one measurement.. it looks valid, to me, but if we can add a collision and potential energy rise, that'll be something worth building, and a raised GPE is gonna make a more compelling point than a manual analysis of some blurry cellphone vids.. you can't really 'see' momentum, after all..

[MrVibrating]

So we have a really intriguing question here - where did that transient net momentum increase come from, and go to, before the sliding mass made it into the center?

Split your momentum into a radial and an angular component.

I've been at pains to point out that there aren't any radial quantities. That's the whole point of keeping the translation speed down to 1 mm/s - so the radial components are orders below the angular magnitudes.

Thus the velocities we're reading - along with all the velocity-dependent fields - are 99.999 % pure angular quantities.

Obviously, if we do find anything useful, then we can design and scale the requisite translation speeds around our calculated margins. But i'm keeping them negligibly-low for now, precisely to keep the angular relationships in focus.

To be honest, my biggest concern until this evening was that i'd only seen this momentum rise when inputting energy, via that 1 mm/s actuator.

Obviously, the assumption is that this linear actuator accounts for all of the input work and subsequent energy rise - that's why i've divided the input energy per meter of radial translation, as 'input energy', by the resulting change in momentum, to plot the unit energy cost of momentum in the previously-posted table.

However, now that we see the plots follow mirror-symmetry in reverse, that concern seems laid to rest - we still have 'input' energy in the form of the CF PE in the outbound mass, but that's stored PE we input earlier, aside from which, the system is now entirely passive.

It's only outputting energy...

And yet the net system momentum more than doubles again, exactly as it did on the way in!

So my fears that it might, instead, transiently lose as much momentum on the way back out, as it gained on the way in were unfounded - it's fully time-symmetrical, and the tabled data can be read up and down equally validly..

I admit, last time i claimed non-constant system momentum i was mistaken. And also, the time before that. And all the other times before that too. And every time i claimed it was really irrefutable this time, and went off on one ranting about non-dissipative loss mechanisms.

But this time... i'm, like, super, super seriously, dudes... this really really looks like a passive, reactionless rise in net system momentum..

If we can harness it, we'd gain energy from its rising ambient velocity, relative to gravity's stasis..

[MrVibrating]

Here's that last sim for those with WM2D, attached below... (it pauses in the middle, just flip the two black switches to swap the in/out directions and starting RPMs, and hit play).

Or else, here's a fully automated version incl. the data.

..just hit play when it pauses in the middle..


...and for those without WM, here's a GIF animation.

[ME]

To be honest, my biggest concern until this evening was that i'd only seen this momentum rise when inputting energy, via that 1 mm/s actuator.

mine too...
Why don't you use a pre-loaded spring so you know exactly the energy input to work against the centrifugal force.

[MrVibrating]

mine too...
Why don't you use a pre-loaded spring so you know exactly the energy input to work against the centrifugal force.

That's kinda moot now, since we're not inputting energy when it comes back out - yet we still get the momentum rise.

However, we know definitively that the rise in net KE represents all of the input work - unless we're invoking some other symmetry break, all of the rise in energy must be input energy.

Similarly, in reverse, all of the drop in energy must be dissipated by the actuator as the mass falls back out under CF.

Using a spring to store a pre-determined quantity of PE is OK once we have well-defined parameters to aim for. For now though, they cause precisely the problems that this test was intended to overcome - if the mass is allowed to accelerate radially, then we charge headlong through all this striking scenery without noticing any of it, much less having a chance to analyse its potential tactical advantages..

For the past few years, that's all i've been doing - heaving masses in and out with springs, GPE's etc. etc. - and i never noticed this was causing a non-constant system momentum... because all the action of interest was over in a blur.

But this is an intrinsically time-dependent effect, and so stretching it out over 1,000 or 2,000 seconds at a sloooow 1 mm/s radial translation, 1 RPM and ten meter radius, allows us to succinctly and accurately map out all the territory here - at constant radial speed / distance. Like a microscope slide, this is a microcosm of an inertial torque. Smeared out in time and space to accentuate and highlight its features and dynamics..

To make a pretty solid analogy, you could replicate the results here on the back of a (large) envelope... the most complicated aspect is the inter-reaction between the two point-inertias. The data in the table above, and metered in the sims, is just a sequence of integrals, which could even be calculated quasi-statically, if you had the time... but then that's why we have sims.

So springs, yes, definitely useful, but in the first instance i simply want to see the territory, against a linear, consistent time/space metric. Interacting angular inertias / momenta, with minimal contamination from radial components (not least rapidly-accelerating spiky bouncy ones).

[MrVibrating]

OK i've hit a problem i could use some advice with:

- WM2D is modelling momentum gains in ordinary elastic collisions under certain circumstances

- since i'm currently trying to apply a collision as a means of distributing momentum, it's critical to get accurate behaviour, or else i'll be wondering why builds don't work..

- anyone with WM, or any other sim for that matter, with gravity off, try flying a 1 kg mass at 1 meter/sec into a static but free-floating 3 kg mass, monitoring the resulting distribution of momentum.

I'm getting momentum gains as a function of material elasticity - at fully-elastic, momentum doubles, at semi-elastic momentum rises 25%, and to get constant momentum i have to set elasticity to .250... however this also means dissipating a load of KE away...

For some reason it seems we can have CoM or CoE, but not both together?

[Gregory]

OK i've hit a problem i could use some advice with:

- WM2D is modelling momentum gains in ordinary elastic collisions under certain circumstances

- since i'm currently trying to apply a collision as a means of distributing momentum, it's critical to get accurate behaviour, or else i'll be wondering why builds don't work..

- anyone with WM, or any other sim for that matter, with gravity off, try flying a 1 kg mass at 1 meter/sec into a static but free-floating 3 kg mass, monitoring the resulting distribution of momentum.

I'm getting momentum gains as a function of material elasticity - at fully-elastic, momentum doubles, at semi-elastic momentum rises 25%, and to get constant momentum i have to set elasticity to .250... however this also means dissipating a load of KE away...

For some reason it seems we can have CoM or CoE, but not both together?

Don't worry, there is no problem! :)

I think you are getting that result because you are measuring total momentum of the two bodies without +/- signs.
If you create a graph and rewrite the formulas yourself to add together for example M in the x direction, so Mbody1x + Mbody2x, then you should get a conserved value.
But if you use this instead: Abs(Mbody1x) + Abs(Mbody2x), then you will get a gain, quite like as you described.

And the explanation is that scientist and physicist assume that you can only get a real result by calculating sums with +/- signs. Although in Abs() you can think you have a gain, but it is not real in a scientific sense, unless you can engineer a machine which can make use of that. But that machine would most likely need to accomplish an N3 violation in order to do that. So, therefore that should be not possible...

You can think about elasticity like a kind of "momentum/motion conservation parameter" in collisions. A ball dropping from a height... At 1.00 you can have infinite number of collisions with the floor and your ball will still jump back to the same height. At 0.00 it doesn't bounce back even for the first time. A realistic simulation value is between 0.05 - 0.95, or if you want to be stricter you can use the range 0.2 - 0.8. Anything above 0.99 or below 0.01 is being in wonderland smoking vampire dust ;)

I usually use 0.95 if I want a good elastic collision, and 0.05 if I don't want a rebound.

[Fletcher]

This might be useful to you.