Double Pendulum Power

[nybtorque]

You are going to find out shortly that this 'power' is simply an illusion of your flawed analysis.

Any attempt to extract it WILL slow the pendulum down. Once that happens the pendulum has less kinetic energy to exchange for potential energy and the system ends up in a lower potential state. That lower potential is subsequently exchanged for a lower amount of kinetic energy and so on oscillating back and forward until it stops. The total amount of energy that you can extract is equal to the amount of energy it was given to start.

It is ludicrous to analyse in terms of  power (the time derivative of energy) and expect that it can be magically extracted without lowering the total energy state of the system.

@LibreEnergia


I value your feedback since it gives me direction on where to put my effort in explaining the line of thought. I would appreciate though if you could give me a less opinion based explanation to why it's "ludicrous" to integrate power over time and calculate work performed.


I do agree that if you take energy out the pendulum WILL SLOW DOWN and that kinetic energy WILL have to be replaced.


If we leave the energy extracting aspect, do you agree with the free fall/artificial gravity analogy? I.e the inner pendulum mass being in constant acceleration (varying in direction and size)?


Then, think about it this way. How much energy does it take to stop a 1 kg mass in free fall? Well, anything from 0 J to whatever depending on the speed it have reached due to gravity (E=mgh=mv^2/2). Then again, think about it as if you always reduce the acceleration 50% by a generator and book the energy difference. How much energy will you book? Well, E=mgh/2 of course....


As you can see, this example is only limited by "h". The mass will continue to accelerate, although at a slower rate, gain velocity, etc. All because of gravity. So, what if "h" is infinite and "g" can be decided by speed of rotation. How much energy can you extract?


I'm only proposing a non-linear model of this example. The concept is used for high-G training already, although at lower rates...


Regards NT

[nybtorque]

Hi nybtorque,
can you please post your paper as a pdf file. I have difficulty reading it on where it is now, as well as downloading.
But otherwise, very fascinated with your concept!
May be it will be beneficial to connect your oscillating ring to a pivoting arm, to increase the leverage?
Regards

I'll try to post it below.


Pivoting arms of different length is part of the concept. It could be beneficial depending on what you want to achieve. If you want angular amplitude short arm is best, if you want linear amplitude a long arm is better. The power will be the same though.

[LibreEnergia]

I do agree that if you take energy out the pendulum WILL SLOW DOWN and that kinetic energy WILL have to be replaced.

That is all you need to realise.

You cannot use free fall of gravity to replace the energy lost. For that to occur the system would need to have gravitational potential to allow it to fall, but the maximum of potential reduces at exactly the same rate as the energy is dissipated either by a generator or by friction.

Build a simulation that has a damping force proportional to the angular velocity at the pivots and you'll see that.

[nybtorque]

That is all you need to realise.

You cannot use free fall of gravity to replace the energy lost. For that to occur the system would need to have gravitational potential to allow it to fall, but the maximum of potential reduces at exactly the same rate as the energy is dissipated either by a generator or by friction.

Build a simulation that has a damping force proportional to the angular velocity at the pivots and you'll see that.

Well, that is not really ALL I have to realize!! Of course friction in the pivots will make the pendulum stop eventually. Friction in the outer pendulum needs so be replaced continually. With the inner pendulum it's a bit more complicated. You need to consider that friction is in the opposite direction of velocity, but that acceleration is more or less in the opposite direction of velocity half of the time as well, so friction is actually more or less neutral to power. This is the reason why the potential does not reduce in the same rate as the kinetic energy. Friction actually has direction (DC), but power has not and an if you replace friction with a generator you will get AC-power.

[telecom]

Hi NT,
I'm not sure this statement is correct:
The interdependencies between the two pendulums continuously exchanging
kinetic energy as they oscillate is complex. The two pendulums transfer
momentum between themselves in both directions as described by the Euler
Lagrange equations earlier. If we try to force the outer pendulum into a
certain speed or movement, we will no doubt disturb the inner pendulum as
it transfer momentum back. Constant rotation of the outer pendulum will
simply not do.
The way I see it, the outer pendulum simply doesn't "see" the inner pendulum.
It keeps rotating in equilibrium (less friction) according to the first law of motion:
2. Rotational equilibrium:When body is not rotating at all or its rotating at constant rate it is said to be in rotational equilibrium. This is Newton's first law of motion,equilibrium.

To activate the inner pendulum with use the reaction of the axis of the outer pendulum by allowing the axis to move freely in one direction, being attached to the pivot of the inner pendulum.
What do u think?
Regards!