Big try at gravity wheel

[Red_Sunset]

..............................................................................
I hope that goes some way to answering your question.   

Hi Frank,

Thanks for your write-up effort.
It is a nice theory that we can identify energy in several component parts. It appears like a sensible theory.
So I have no argument with any of what is presented, although I do not see where it takes us any further than where we were before you posted it.
There is more to come ?, or should I do more digestion to satisfy my hunger

My interest lies in how this can provide a conservation workaround as you initially theorized to.

Regards, Red_Sunset

[Grimer]

Hi Frank,

Thanks for your write-up effort.
It is a nice theory that we can identify energy in several component parts. It appears like a sensible theory.
So I have no argument with any of what is presented, although I do not see where it takes us any further than where we were before you posted it.
There is more to come ?, or should I do more digestion to satisfy my hunger

My interest lies in how this can provide a conservation workaround as you initially theorized to.

Regards, Red_Sunset

I'd already prepared the following offline before I read your post so I'll paste it and add any other comments at the end.


==============================================================

To sum up the diagram of a previous post showing the paths of a cicular pendulum and a cycloid pendulum:


The cycloid pendulum arrives at the lowest point of the arc having the NG 2nd derivative energy of the NG drop length.


The circular pendulum on the other hand arrives with both the NG 2nd derivative energy and a EG 3rd derivative contribution.


How can this 3rd derivative energy be visualised?


When I was a young design engineer indeterminate structures were analysed with an approximate method called Moment Distribution invented by a US engineer, Hardy Cross, a method long since superceeded by computers and Finite Element Analysis.


The forces at the end of a member were diagramatically represented not only by the tension and compression straight vector arrows but in addition by circular arrows which denoted moment or twist.


So the circular pendulum shaft has NG energy and EG 3rd derivative twist energy. It is this twist energy, this moment energy that is released to take the bob higher than its start position as it switches at nadir junction from the slow circular track to the fast Brachistochrone track.
==============================================================


To actually carry out an experiment to demonstrate this would be a herculean task since one would have to have a pendulum shaft with asymmetric properties; stiff on the circular pendulum side and flexible on the cycloid pendulum side.


However, if one thinks about it one can see how a stiff pendulum shaft will be given a moment as it falls since there is a well know phenomena which demonstrates this in spades.


And that phenomena is the falling chimney which breaks in the middle as it falls. Think about it.


It breaks because its subjected to a bending moment which is sufficient to exceed its bending strength. The shear size and weakness of the chimney shows this up whereas with the pendulum shaft everything takes place below the threshold of perception - but not below the threshold of reason. 


No doubt sourpuss TK aka AS would like to call that rationalizing. 

[minnie]

Hi Grimer,
            well explained, even made sense to me. Thank you.
                                 John.

[Grimer]

Hi Grimer,
            well explained, even made sense to me. Thank you.
                                 John.

Thanks very much, minnie. 


I wish the people on BesslerWheel.com could understand me as well as you do.

[conradelektro]

And that phenomena is the falling chimney which breaks in the middle as it falls. Think about it.

It breaks because its subjected to a bending moment ....

I would like to offer an alternative explanation for the falling chimney:

See, chimneys are jerks who jerk off during the night because they do not like being watched jerking off.

Usually chimneys are blown up during the day. And when the chimney falls it wants to jerk off one last time. But the chimney cramps up in daylight and breaks because he applies a too great bending force.

Greetings, Conrad