Hypothesis .. Raising GPE without using Law of Levers ? ..

[daxwc]

It's a fascinating interplay where time intertwines with inertia and energy flow. However, this assumes that the Conservation of Energy holds true. In reality, it may be more accurate to rely on the Conservation of Momentum; which remains valid in closed systems without external forces.

[daxwc]

Fletcher: The sim experiment is a euphemism for two oppositely placed one-way swingers reacting to an equal and opposite impulse ( the bounce, or pump and dump, analogies ) to potentially show the physical benefit of a free and fast lifting outside of classical mechanics WD and Law of Levers constraints - and in my mind-sim this gives rise to an inevitable increase in GPE to be put to useful purpose as free torque, and down-streaming it a wheel that must gain in angular momentum and KEr ..

The ' trick ' is in how mechanically the repeating " bounce and recovery " input is generated and managed in a dynamic revolving environment - not all bounce mechanisms are created equal .. imo ..

I hear you and agree maybe. So you have two radius weights dump and pump mechanical energy back through the middle at a shorter distance. Radius distance is shorter than circumference distance.

[Gregory]

Hi all,

I tried to think through this in more detail, and arrived somewhere.
Yes, johannesbender, you are right that work done can be positive or negative number as well.

For example if you lift a weight with your hands, then work done on the weight will be a positive number, and work done on your muscles will be a negative number.
Or we can envision a point mass going through a force field, which can be gravity, CF, magnetic, or anything... From the perspective of the point mass, if it is accelerated, then WD is positive on the mass, but if it's decelerated then WD is negative on the mass.

After that, I think the correct way to understand this cart & swingers experiment is as follows:
- We have a cart with two swingers, this is the first component of the experiment. (Cart)
- We also have a driver/controller system, this is represented by the accelerating/decelerating forces, this is the second component. (System)

I wanted to add a few additional thoughts I forgot. Not sure if this is useful or anything, just got back on my mind...

1. I think the plus or minus signs of WD can be also somewhat up to interpretation. The standard and most logical choice is to assign a plus sign when an object or system gains energy, and assign the negative when it looses energy. However, if I want to think about this in the opposite way, I certainly can... But then I have to do this with all the math and everything connected, and make sure that things stay consistent in every way. So, I have to have a very good reason if I choose to do something like this… Like I can make the negative side of a coordinate system positive, I can flip the signs if I want, but I need a good reason why I am doing that.

2. In the case of the accelerating and decelerating forces for the cart, I think it's possible to interpret the forces to work with the same sign, like I spend energy twice, both for starting and stopping the cart, and doesn't receive back anything. It's totally legit if the system can be designed this way. However, this does not change what happens with the cart. Also, not sure if such a system would be useful...

3. In a wheel format the cart with the swingers becomes a wheel with many swingers. But the accelerating and decelerating forces (aka the System) also becomes the wheel itself, or at most some subcomponent of it, like the a-prime, a speed variator, or some kind of controller mechanism, etc. This might complicate things, not sure to be the same thing as the linear cart & swinger anymore...
In case the controller mech is something mundane and directly connected to wheel output, then most likely the same currency will just go from one pocket to another and back. An enlightened PM seeker (or another one who already succumbed to the dark side) would want something different, something more heavenly or ritual, like a controller which is not a function of wheel output. Not really part of the wheel at all, but the same time also somehow a component of it. That would be the real deal! But anyway, it sounds like black magic... 8]

[daxwc]

Gregory: 2. In the case of the accelerating and decelerating forces for the cart, I think it's possible to interpret the forces to work with the same sign, like I spend energy twice, both for starting and stopping the cart, and doesn't receive back anything. It's totally legit if the system can be designed this way. However, this does not change what happens with the cart. Also, not sure if such a system would be useful...

This is no different than driving 1000 miles east then turning around drive 2000 miles west then turning around and drive 1000 miles east again. I have done no work but used a lot of energy. An example of how energy usage and work aren’t always directly correlated.

[Gregory]

Gregory: 2. In the case of the accelerating and decelerating forces for the cart, I think it's possible to interpret the forces to work with the same sign, like I spend energy twice, both for starting and stopping the cart, and doesn't receive back anything. It's totally legit if the system can be designed this way. However, this does not change what happens with the cart. Also, not sure if such a system would be useful...

This is no different than driving 1000 miles east then turning around drive 2000 miles west then turning around and drive 1000 miles east again. I have done no work but used a lot of energy. An example of how energy usage and work aren’t always directly correlated.

Yes, that's an interesting example daxwc. Thanks for mentioning!
Right, In each part of the travel work was done on the car, it travelled somewhere in all three trips.
But at the end it didn't go anywhere and arrived just where it started, and the sum of the work is zero. And as you said, energy was used to go nowhere at the end. Which is totally true... On the other hand it still went somewhere, it's just not necessary useful.
Maybe depends on what else the driver did apart from driving without reason.

[Fletcher]

...

3. In a wheel format the cart with the swingers becomes a wheel with many swingers. But the accelerating and decelerating forces (aka the System) also becomes the wheel itself, or at most some subcomponent of it, like the a-prime, a speed variator, or some kind of controller mechanism, etc. This might complicate things, not sure to be the same thing as the linear cart & swinger anymore... No, imo it's not the same anymore imo - I'll try an explain why I think not below ..

In case the controller mech is something mundane and directly connected to wheel output, then most likely the same currency will just go from one pocket to another and back. Yes, Conservation of Energy applies at the local level ..

An enlightened PM seeker (or another one who already succumbed to the dark side) would want something different, something more heavenly or ritual, like a controller which is not a function of wheel output. Not really part of the wheel at all, but the same time also somehow a component of it. That would be the real deal! But anyway, it sounds like black magic... 8]

Thanks for making the dampener springs-pushing swinger sim Gregory, as a further check test etc ( wow, there are some complicated formulas in there that took some working out by you, kudos ) - they hopefully help clarify or eliminate some thoughts about mechanical possibilities, or not, as the case may be - fwiw we all know springs store energy as elastic PE and release it as KE - even a perfect spring can not escape from Conservation of Energy Law - that's why I made the original pump and dump sims activated by impulse/momentum transfer ( constant f * t = m * v ) and not springs energy transfer per se - then it was necessary for me to postulate a source of momentum as a part of the wheel " system ", but external to it, that could activate the system to give the swingers their PE lift and torque - this is theoretically a replenishable momentum ( i.e.. quasi energy ) source which is constantly replenishing from an inexhaustible momentum sink/well - then in theory the Conservation of Energy and Momentum Laws still hold true at the larger earth frame of reference ( FOR ) but not appear to at the local wheel in isolation level where a wheel gains in angular momentum and rpm etc ..

P.S. you could possibly if you feel inclined replace the dampener springs book ends with your previous colliding momentum blocks with elasticity set to 1.00000, as a thought - but I suspect the limited program and computer FOR will distort things ( that's why I'm not sure a sim could show a local violation of Conservation of Energy, or Momentum for that matter, for a full wheel ) ..

So imo your point 3. sums the directions open to us nicely ..

My hypothesis is about lifting weights outside of classical mechanics confines of leverage applications etc - and this " lift to PE " should be fast and easy, with low to no energy cost penalty to get the required PE to torque gain - and this process of cause and effect leads to the quick acceleration of a wheel which gains in momentum and RKE and sustains its self-movement ..

.. I think most of us still following this thread will probably agree by now that if we had just a wheel with multiple paired swingers ( n.b. with currently no way to activate the " bounce effect " yet ) and I was to put my hand on the rim and give it a quick push without releasing the rim then some swingers would raise up and lock-out into torque .. I think we can safely agree on that, especially if we don't dive down the rabbit hole of where that acceleration and deceleration came from, or cost, just yet ..

........................

So walking it back a bit, in my theory the A-prime is the activator or initiator of the required " bounce " to set the swingers ( replaces my hand push ) - it/they are inside the wheel but do not physically or mechanically connect to any swingers - they just share a home, like housemates - both the A-prime(s) and the swingers are part and parcel of the " local system " - the A-prime is gravity activated causing it to fall relatively slowly, closing and opening again to reset - the A-primes inertial action causes the wheel axle to jerk/pulse up and down [ i.e. pulls the whole wheel ( including the A-prime and swingers ) down, and then it rebounds upwards thru the tension/compression forces in the floor to ceiling supports/pillars restoring the axle height ] - this is when the wheel system dips into the external earth momentum sink/well to provide the " energy " to be outputted by the wheel system as external work, accelerate, and sustain its self-movement etc ..

fwiw, previously I used wheel supports attached to fictitious sprung floor and ceiling plates in my sims to represent the ideas I am proposing above about a sink/well of movement - without any real conviction that a sim could reach beyond the confines of Conservation of Energy and Momentum at such a small local level inside my computer screen - but it could maybe conceptually help convey the concept I have been advocating of that external momentum sink/well to continually draw from ..

ETA .. strangely enough, my thoughts are that it does not matter imo how far upwards the axle is restored to ( compared to fall distance ) in vertical height at each A-prime pulse and recovery stroke ( with the wheel ) - the whole of wheel system turns by torque bringing the next A-prime into the action zone and and the process of dipping into the momentum well starts again from whatever axle height it is at at that particular moment - the energy slate is wiped clean and the process restarts ..

........................

[johannesbender]

Gregory , I am not sure if the same sign can be used because it changes how the energy calculation has to be done , one is a subtraction from the energy budged and the other an addition to it , (i wont know i am not a math wiz :/ ) using the correct sign is however the correct way though , in wm2d or other places where the formula is entered you simply have to add the rest of the work formula for the direction of the forces etc etc to have the correct outcome .

Daxwc , i agree the passenger/ driver does not really do much work along the distance the car travels , however the car does work no matter where it goes and if it drives in a circle or back and to and ends up at the same place , the car has to do work to travel and stop and that is how the energy is used , it can also use it when stationary however the car wont do work but then engine and moving parts would ...

https://youtu.be/WL7__D14kGc
https://youtu.be/nnMirzeTepQ
https://youtu.be/AUeyJOm0_30
https://youtu.be/zVRH9d5PW8g

[Fletcher]

Gregory .. here is your dampened spring sim with a mod - I locked down the right hand side pendulum so it can't swing upwards but the left hand side one can - so it gets full inertia at the start ..

It is increasing in velocity ( and KE ) between stop and starts building up quickly, even with dampened springs ..

It probably has to do with your violet spring formula ( reinserting PE gained as elastic energy ) not adapting as you would have liked - I didn't look too closely but thought you might be interested in a gain ..

[Gregory]

Thanks for making the dampener springs-pushing swinger sim Gregory, as a further check test etc ( wow, there are some complicated formulas in there that took some working out by you, kudos ) - they hopefully help clarify or eliminate some thoughts about mechanical possibilities, or not, as the case may be - fwiw we all know springs store energy as elastic PE and release it as KE - even a perfect spring can not escape from Conservation of Energy Law - that's why I made the original pump and dump sims activated by impulse/momentum transfer ( constant f * t = m * v ) and not springs energy transfer per se - then it was necessary for me to postulate a source of momentum as a part of the wheel " system ", but external to it, that could activate the system to give the swingers their PE lift and torque - this is theoretically a replenishable momentum ( i.e.. quasi energy ) source which is constantly replenishing from an inexhaustible momentum sink/well - then in theory the Conservation of Energy and Momentum Laws still hold true at the larger earth frame of reference ( FOR ) but not appear to at the local wheel in isolation level where a wheel gains in angular momentum and rpm etc ..

P.S. you could possibly if you feel inclined replace the dampener springs book ends with your previous colliding momentum blocks with elasticity set to 1.00000, as a thought - but I suspect the limited program and computer FOR will distort things ( that's why I'm not sure a sim could show a local violation of Conservation of Energy, or Momentum for that matter, for a full wheel ) ..

Yes, I went crazy mode with those formulas. :D
Yes, you're right that impulse/momentum/F * t is different than work/energy, thus springs will always stay within the framework of energy math, etc. On the other hand, if you think about a bit, it doesn't really matter how (by which method) I start the cart, it will inherently start with a packet of energy and momentum, whichever way I initiated that. We can set the starting energy/momentum whatever (way) we want, I think that by itself doesn't change the experiment.

I just wanted to see where we arrive if I turn back the GPE to kinetic energy. Well, CoE happened... the GPE is part of the contract, not an outsider.
Yes, momentum route might be somehow different. I will post such a version if I come up with that.

So imo your point 3. sums the directions open to us nicely ..

My hypothesis is about lifting weights outside of classical mechanics confines of leverage applications etc - and this " lift to PE " should be fast and easy, with low to no energy cost penalty to get the required PE to torque gain - and this process of cause and effect leads to the quick acceleration of a wheel which gains in momentum and RKE and sustains its self-movement ..

Passive lift or lift to PE is a nice concept. Would be a charm to see it open the gate...

.. I think most of us still following this thread will probably agree by now that if we had just a wheel with multiple paired swingers ( n.b. with currently no way to activate the " bounce effect " yet ) and I was to put my hand on the rim and give it a quick push without releasing the rim then some swingers would raise up and lock-out into torque .. I think we can safely agree on that, especially if we don't dive down the rabbit hole of where that acceleration and deceleration came from, or cost, just yet ..

Yes, sure.

So walking it back a bit, in my theory the A-prime is the activator or initiator of the required " bounce " to set the swingers ( replaces my hand push ) - it/they are inside the wheel but do not physically or mechanically connect to any swingers - they just share a home, like housemates - both the A-prime(s) and the swingers are part and parcel of the " local system " - the A-prime is gravity activated causing it to fall relatively slowly, closing and opening again to reset - the A-primes inertial action causes the wheel axle to jerk/pulse up and down [ i.e. pulls the whole wheel ( including the A-prime and swingers ) down, and then it rebounds upwards thru the tension/compression forces in the floor to ceiling supports/pillars restoring the axle height ] - this is when the wheel system dips into the external earth momentum sink/well to provide the " energy " to be outputted by the wheel system as external work, accelerate, and sustain its self-movement etc ..

fwiw, previously I used wheel supports attached to fictitious sprung floor and ceiling plates in my sims to represent the ideas I am proposing above about a sink/well of movement - without any real conviction that a sim could reach beyond the confines of Conservation of Energy and Momentum at such a small local level inside my computer screen - but it could maybe conceptually help convey the concept I have been advocating of that external momentum sink/well to continually draw from ..

ETA .. strangely enough, my thoughts are that it does not matter imo how far upwards the axle is restored to ( compared to fall distance ) in vertical height at each A-prime pulse and recovery stroke ( with the wheel ) - the whole of wheel system turns by torque bringing the next A-prime into the action zone and and the process of dipping into the momentum well starts again from whatever axle height it is at at that particular moment - the energy slate is wiped clean and the process restarts ..

........................

Would love to see such a wheel!
The A-prime is something I not yet concluded how to think or deal with. Probably needs a lot of experimentation.
One disadvantage though, it adds more mass/MoI to the wheel, making all acceleration attempts less powerful/weakened, while a spring variator doesn't do that, no additional mass...
On the advantage side though, the A-prime doesn't mess with energy or RKE destructively, while a spring variator maybe does in certain cases.
Would be nice to have a best of all worlds scenario...

[Gregory]

Gregory , I am not sure if the same sign can be used because it changes how the energy calculation has to be done , one is a subtraction from the energy budged and the other an addition to it , (i wont know i am not a math wiz :/ ) using the correct sign is however the correct way though , in wm2d or other places where the formula is entered you simply have to add the rest of the work formula for the direction of the forces etc etc to have the correct outcome .

What I meant is... that those accelerating/decelerating forces can belong into the same bucket... or can represent superman pushing the cart twice. Once at the start and once more when stopping it. Superman spent energy twice, which is negative work on his muscles twice.
But the cart's side of things remain the same, just standard plus and minus, as usual.
If that makes sense?

[Gregory]

Gregory .. here is your dampened spring sim with a mod - I locked down the right hand side pendulum so it can't swing upwards but the left hand side one can - so it gets full inertia at the start ..

It is increasing in velocity ( and KE ) between stop and starts building up quickly, even with dampened springs ..

It probably has to do with your violet spring formula ( reinserting PE gained as elastic energy ) not adapting as you would have liked - I didn't look too closely but thought you might be interested in a gain ..

Hey Fletcher,

Nice!
I also had a couple of these when I am building up the experiment...

Yeah, the problem is that in this case you swung the pendulum up once, but invested its PE content many times repeatedly into the cart going backward, doing this via the violet spring enchantment...

I love enchanted springs, btw! :)
But I'm afraid this is unrealistic in more ways.
One is rising the pendulum once and using up its GPE more times.
Another, the spring formula is experimental (there is a hard coded constant in it) and will add more and more deviation with each repetition.

Plus the violet spring works in a way that you compress it for zero energy cost, but then it gives you an additional acceleration. Which is a very powerful enchantment if used out of context. :D
So, it's a cheat. The way this is designed at the moment postulates that the pendulums have to be lowered every time... to be close to any realism.

I will try to correct the spring formula, not sure to be successful.
On the other hand I have another swinger wheel test to post, a crazy one actually with some interesting stuff...
Stay tuned, I'll post it some time!

[Fletcher]

Gregory , I am not sure if the same sign can be used because it changes how the energy calculation has to be done , one is a subtraction from the energy budged and the other an addition to it , (i wont know i am not a math wiz :/ ) using the correct sign is however the correct way though , in wm2d or other places where the formula is entered you simply have to add the rest of the work formula for the direction of the forces etc etc to have the correct outcome .

What I meant is... that those accelerating/decelerating forces can belong into the same bucket... or can represent superman pushing the cart twice. Once at the start and once more when stopping it. Superman spent energy twice, which is negative work on his muscles twice.

But the cart's side of things remain the same, just standard plus and minus, as usual.

If that makes sense?

You said it before Greg, and we all know it to be true, and why the Conservation Laws capture everything and not just our swinger carts in isolation etc ..

Newton's 3rd Law of action and reaction ..

In the first law, an object will not change its motion unless a force acts on it.
In the second law, the force on an object is equal to its mass times its acceleration.
In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

His third law states that for every action (force) in nature there is an equal and opposite reaction. If object A exerts a force on object B, object B also exerts an equal and opposite force on object A.

So the Energy Budget will balance if all bodies are taken into consideration ..

* However, if we want to assign positive work and negative work to a scalar that fine - it's just tracking and relating to the body in motion and will be equaled out by the opposite actions as Newton and Gregory say ..

In my sims I have shown that if momentum is given and taken away again such that the swinger gains a set velocity and KE and then loses it down to zero, then in this special case the WD does not equal the KE ( whether viewed as positive or negative work ) for each leg - the WD in the 2nd leg is less than the KE lost in the 2nd leg, and the WD in the 1st leg is greater than the KE gained in the 1st leg - the sims and table shows this repeatable trend ..

But the requirement for this disparity in the Work-Energy Theorem only occurs when we input equal and opposite Momentums ( Impulses ) to change velocities up and then down again, of non-rigid articulated bodies demonstrating partial or variable MOI characteristics ..

IOW's, in reference to Newtons 3rd the earth background compensatorily moved disproportionately to balance the bigger picture Conservation Laws and Work-Energy Equivalence Principle FOR, imo .. * this is what these sims were about, not so much the raising of GPE and setting to torque byproduct of these sets of sim experiments ..

* Will have to dig out my A-prime verses ordinary piston-like activator sims for comparability purposes - to hopefully show why I think Storks Bills ( SB's ) have a special ability of note in relation to harvesting this theoretical momentum transfer I theorize about to cause Work-Energy Theorem to tail spin - I will go looking for them when I clear some decks ..

......................

[daxwc]

Fletcher: IOW's, in reference to Newtons 3rd the earth background compensatorily moved disproportionately to balance the bigger picture Conservation Laws and Work-Energy Equivalence Principle FOR, imo .. * this is what these sims were about, not so much the raising of GPE and setting to torque byproduct of these sets of sim experiments ..

A sim can’t show Earth's pushback because it doesn't model the Earth itself; it’s limited to the local interactions it’s programmed for. The idea of “Earth compensatory movement” is just a theoretical abstraction, not something a sim can directly demonstrate or am I missing something?

So are you suggesting that the equations inherently account for concepts like Earth's compensatory movement because they were derived from real-world experiments where these dynamics naturally occur?

[Gregory]

You said it before Greg, and we all know it to be true, and why the Conservation Laws capture everything and not just our swinger carts in isolation etc ..

Newton's 3rd Law of action and reaction ..

In the first law, an object will not change its motion unless a force acts on it.
In the second law, the force on an object is equal to its mass times its acceleration.
In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

His third law states that for every action (force) in nature there is an equal and opposite reaction. If object A exerts a force on object B, object B also exerts an equal and opposite force on object A.

So the Energy Budget will balance if all bodies are taken into consideration ..

* However, if we want to assign positive work and negative work to a scalar that fine - it's just tracking and relating to the body in motion and will be equaled out by the opposite actions as Newton and Gregory say ..

Newton's laws should not be violated! :)
Right, it was likely too far of a stretch on my part. If I don't count coordinate direction then I can perhaps dismiss the signs, but for what...
I didn't take the bigger picture into account, so even if I design a mechanism or system decreasing its energy twice to start and stop a mass, still from the bigger picture and FoR, there will be always the usual pairs of forces present, action-reaction. Or at least this is always expected to be the case. Unless you have an universal sink/well anomaly or something...

In my sims I have shown that if momentum is given and taken away again such that the swinger gains a set velocity and KE and then loses it down to zero, then in this special case the WD does not equal the KE ( whether viewed as positive or negative work ) for each leg - the WD in the 2nd leg is less than the KE lost in the 2nd leg, and the WD in the 1st leg is greater than the KE gained in the 1st leg - the sims and table shows this repeatable trend ..

But the requirement for this disparity in the Work-Energy Theorem only occurs when we input equal and opposite Momentums ( Impulses ) to change velocities up and then down again, of non-rigid articulated bodies demonstrating partial or variable MOI characteristics ..

IOW's, in reference to Newtons 3rd the earth background compensatorily moved disproportionately to balance the bigger picture Conservation Laws and Work-Energy Equivalence Principle FOR, imo .. * this is what these sims were about, not so much the raising of GPE and setting to torque byproduct of these sets of sim experiments ..

* Will have to dig out my A-prime verses ordinary piston-like activator sims for comparability purposes - to hopefully show why I think Storks Bills ( SB's ) have a special ability of note in relation to harvesting this theoretical momentum transfer I theorize about to cause Work-Energy Theorem to tail spin - I will go looking for them when I clear some decks ..

......................

Ok, I understand the main message is that equal but opposite impulses cause this deviation between WD and KE, and GPE comes as a result or by product of this process. So we assume that the positive and negative impulses cancel out for the impulse source, meaning no or little loss of motion/momentum, while we ended up with a potential accelerating capability in the form of GPE, which can be used to supply torque... It's fine, actually even more than fine. It should be possible to make a cart sim where GPE is used to supply an increased impulse with each cycle, which should in theory result in an accelerating cart, hhmm... Or a wheel experiment of this process, I have one next on my list... Right, that's the main goal.

Probably I was too much focused on the GPE, was interested to investigate and see if anything else can be found.
Btw, I think I corrected the violet spring, but probably not much use for it. I don't mind, it was a good exercise.

[Fletcher]

Fletcher: IOW's, in reference to Newtons 3rd the earth background compensatorily moved disproportionately to balance the bigger picture Conservation Laws and Work-Energy Equivalence Principle FOR, imo .. * this is what these sims were about, not so much the raising of GPE and setting to torque byproduct of these sets of sim experiments ..

A sim can’t show Earth's pushback because it doesn't model the Earth itself; it’s limited to the local interactions it’s programmed for. Imo, it's a matter of the scale to detail ratio required imo ..

The idea of “Earth compensatory movement” is just a theoretical abstraction, not something a sim can directly demonstrate or am I missing something? More than a theory imo - at the planetary and cosmic scale it is well modeled by Newtons Laws and Einstein's Theories .. it is used everyday in satellite slingshot maneuvers etc where a large planetary body's momentum is used to accelerate a smaller orbiting body ( increasing its outward velocity ) as it enters the gravity field and exits - the satellite gains some of the larger body's momentum while the larger one loses a little momentum ( proportional to mass ) - sims of a different sort are used for these large scale interactions of action and reaction mechanics ..

So are you suggesting that the equations inherently account for concepts like Earth's compensatory movement because they were derived from real-world experiments where these dynamics naturally occur?

Actually the opposite dax .. in our usual daily doings I suggest we only ever deal with half the equations, and not the whole earth context ( which is part of a bigger context ) - we only consider the object in the gravity field and the force acting on it, or the work done on it etc - we know the earth is equally effected ( proportional to mass ) but as I said earlier when we drop a ball when do we ever calculate how much PE was lost and how much KE was gained by the earth ? - never, unless we are using celestial mechanics and larger scale where it has relevancy perhaps ..

We do not even consider the other half of the transaction in our earth surface bound context because our FOR doesn't change for us, therefore it is functionally and practically irrelevant to us and the outcomes we wish to predict with the classical mechanics equations of motion etc ..

B. would likely never have thought about these things as a possible plausible and useful energy source for his runners ( it was just a conservative force OOB gravity wheel right ?! ) - but Kepler's two-body problem was already in circulation and Newton had built on that in his Principia Mathematica prior to B's. runners solution - but making a lucid connection to a runners replenishing energy supply would be even more of a big stretch then, than it is today with that practical experience of decades of space programs etc ..