Double Pendulum Power

[gyulasun]

Single arm version of nybtorque's double pendulum continuos drive machine.
Anybody curious? I was.


Vince

Hi Vince,

Thank you for showing the single arm version.  I am curious...  so if you could share your findings or impressions, that would be very helpful.

Greetings,  Gyula

[nybtorque]

Your "model" can be falsified simply by observing that the "double pendulum", more commonly known as a Chaotic Pendulum, always comes to a stop.

Consider this: If you had really sticky bearings the thing would swing a few times and slow down and stop. Right? SO decrease the friction a little bit. Now it takes a bit longer to run down and stop. Reduce friction even more, even put it in a vacuum. It takes a bit longer... but it still stops.

Why? Because the friction eventually dissipates _all_ the energy you put in with your initial starting impulse... and nothing comes in from anywhere to replace it.

If there were _any_ excess energy in the system, by reducing friction to some arbitrarily small value... a value that is less than the magical "incoming" or created power... it would not stop swinging.  But it always does. Therefore... there is no extra energy, no excess power coming in.

ANY load you put on the system will make it come to a stop faster.


The physics simulation "Phun" or "Algodoo" even comes with a couple of Chaotic Pendulums as example scenes. If you think that the chaotic pendulum cannot be modeled mathematically... how does Phun do it, by smoke and mirrors?

I think you've misunderstood. Modeling the double pendulum mathematically is EXACTLY what I've done by solving Euler Lagrange numerically using Runge Kutta. I doesn't get much better than that... Preservation of energy sort of comes with the deal. And yes, if you take kinetic/potential energy out of the system it will stop eventually, as in the case of friction.


However. Consider this: You have a double pendulum swinging freely, preserving energy. Then you start increasing friction but ONLY for the inner pendulum. What will happen? Well, the inner pendulum will slow down (act heavier). And by acting heavier it will accelerate less  and therefore exchange less kinetic energy with the outer pendulum during each oscillation. I the end friction will be 1 and the inner pendulum will stop, but the outer pendulum will keep rotating/swinging, preserving it's energy. And keep acting on it's fixture (fixed or a mass free to move) with centrifugal force without any more energy added. Like a single pendulum...


Regards NT

[nybtorque]

I disagree. The system is given a certain amount of energy to start. After that this energy oscillates between kinetic and potential. With no friction it would continue forever. As such it acts as an energy STORE, but it is not GENERATING an excess of energy. If you bleed of the stored energy either by friction or using a generator, it will stop. The total amount of energy dissipated or generated will exactly equal the amount to energy given to it at the start.

Your proposal violates conservation of energy principles. Sorry, it just doesn't happen.

Your math is guilty of the same double counting error that Wayne Travis makes with his non working device, except your analysis is rather more complex.

As I said, using Euler Lagrange guarantees that the math is in accordance with the conservation of energy principles. It IS the principles. Do you disagree with the fact that the pendulum masses constantly accelerates (decelerate) as they exchange pot/kin energy, and that Energy=mass*acceleration*distance?


What I have done is to analyze the work performed by the inner pendulum mass using Euler Lagrange and the above basic equation. A flywheel with a constant speed of rotation STORES energy. This is something different. Here we have constantly accelerating masses; a whole different animal and it performs work constantly without energy added. The trick is how to make it useful, and add energy to overcome friction, etc.

[LibreEnergia]

Preservation of energy sort of comes with the deal. And yes, if you take kinetic/potential energy out of the system it will stop eventually, as in the case of friction.

There is no difference energy-wise between a pivot that has friction and a pivot joint containing a generator where the energy generated drives an external load. Both will dissipate energy from the system. Both will cause it to stop.

The pendulum does not simply 'act heavier'.  Any kinetic energy it has will be reduced as it either drives an external load or is dissipated as heat. It CANNOT do both, as in drive an external load and maintain kinetic energy.  The reduced kinetic energy is then translated into less potential energy, and the system eventually stops.

[nybtorque]

There is no difference energy-wise between a pivot that has friction and a pivot joint containing a generator where the energy generated drives an external load. Both will dissipate energy from the system. Both will cause it to stop.

The pendulum does not simply 'act heavier'.  Any kinetic energy it has will be reduced as it either drives an external load or is dissipated as heat. It CANNOT do both, as in drive an external load and maintain kinetic energy.  The reduced kinetic energy is then translated into less potential energy, and the system eventually stops.

Sorry, I've been a bit unclear. My mistake! I agree that friction in the inner pendulum joint drains the inner pendulum of kinetic energy. What I meant is  that it "acts heavier" from the perspective of the outer pendulum.


Do you agree that friction at the inner pendulum joint doesn't drain kinetic energy from the outer pendulum?  Do you agree that if you stop the inner pendulum (go from friction 0 to 1 in an instant) the outer pendulum will keep moving with the kinetic energy it had at that moment (but the inner pendulum kinetic energy will turn into friction/heat)?


But, now, the most important part. How much energy did you actually need to stop the outer pendulum short and drain it from its kinetic energy (mv^2/2). Well, if it was rotating with a constant speed, that would be it.


But it's not... It's accelerating (oscillating) with considerable torque. If we take an example: I'm looking at a spreadsheet with a simulation of a 50Hz system with dt=1/1000s. At one particular moment a 1kg pendulum on a 20cm lever has v(t)=25rad/s and a(t)=3000 rad/s^2.  So if you stop it short in an instant, you're right, you only need to drain it of kinetic energy; 12.5 J. BUT you will experience a static torque of 120Nm trying to hold it (thats really hard, but not work per se... .


So, lets imagine instead that you want to reduce both velocity and acceleration by 50% on a continuos basis. Since the mass is still moving you need to take acceleration into account to do that. Of course you can reduce velocity instantly by using 9.38 J of energy (3/4 of the kinetic energy). It will now move at 12.5rad/s instead but still performs work of P(t)=1500W at that velocity and acceleration. To reduce the acceleration from 3000 rad/s^2 to 1500 rad/s^2 you consequently need to apply 750 W at that particular time.


And no, this does not violate the conservation of energy principles. Because we're dealing with the derivatives of energy and speed, i.e. power and acceleration. Much more interesting if you ask me...