Big try at gravity wheel

[MarkE]

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.


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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.
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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. 

Grimer, I see three statements that can be the basis for a testable hypothesis:

1) The cycloid pendulum potential energy at its apogee contains only gravitational potential energy with all gravitational force operating normal to the horizon.
2) A circular path pendulum with a vertical length arm of y1 and bob mass m1 has at its apogee additional "third derivative energy" over and above the potential energy as an otherwise identical cycloid pendulum has.
3) A hybrid pendulum with vertical length arm of y1 and bob mass m1 that follows a circular path on one side of its travel and a cycloid path on the other half of its travel will convert the additional "third derivative energy" of the circular path half to additional gravitational potential energy observable as a higher apogee on the cycloid side than the circular side.

Please correct any of these statements as necessary.  Once we are absolutely clear on the hypothesis I believe that I can define experiments that do not require Herculean efforts.

[Red_Sunset]

Grimer, I see three statements that can be the basis for a testable hypothesis:
1) The cycloid pendulum potential energy at its apogee contains only gravitational potential energy with all gravitational force operating normal to the horizon.
2) A circular path pendulum with a vertical length arm of y1 and bob mass m1 has at its apogee additional "third derivative energy" over and above the potential energy as an otherwise identical cycloid pendulum has.
3) A hybrid pendulum with vertical length arm of y1 and bob mass m1 that follows a circular path on one side of its travel and a cycloid path on the other half of its travel will convert the additional "third derivative energy" of the circular path half to additional gravitational potential energy observable as a higher apogee on the cycloid side than the circular side.
Please correct any of these statements as necessary.  Once we are absolutely clear on the hypothesis I believe that I can define experiments that do not require Herculean efforts.

Hi MarkE,
From my viewpoint, you hit the nail squarely on the head. The cost factor introduced by the cycloid swing path interference will be the prime consideration in the final balance tally.
Red_Sunset

[MarkE]

Red_Sunset, I think we have real progress here because I think that Grimer has said enough to that we can state his hypothesis clearly and unambiguously.  What we need now is for Grimer to either agree with the hypothesis as stated or make needed changes so that it accurately reflects his ideas.  I am optimistic that once we have the hypothesis nailed down in language everyone agrees on that I can propose experiments that will not require high cost or difficulty.

[Grimer]

Hi MarkE,
From my viewpoint, you hit the nail squarely on the head. The cost factor introduced by the cycloid swing path interference will be the prime consideration in the final balance tally.
Red_Sunset

Hi Sailor, 


Yep. I have to admit that in spite of being thorough pissed off with him and suspecting him of being an agent for Big Oil -
- a Battle of Waterloo carrier pigeon ready to fly home to his master as soon as it's clear that Gravity's not conservative -
- that he has a point.


Of course if the logic is sound then we don't need an experiment, do we.
We don't need experiments to show that the square on the hypotenuse is equal to the sum of the squares on other two sides, do we.


If experiment fails to confirm the many cheerful facts about the square on the hypotenuse then so much the worse for the experiment.


I suppose its useful to have an experiment to show to those too dim to follow a logical argument.
We'll have to call it the Didymus experiment, eh! 

[MarkE]

Grimer, no argument by itself is going to make all of the observations that gravity seems to operate conservatively go away.  If in the time of Euclid someone had shown that beyond some point there appeared to be no more prime numbers, and try as anyone could they could not locate additional prime numbers, then Euclid's assertion that there are an infinite number of primes would have been in great jeopardy.  Therefore it is insufficient to simply declare that you have an exception to the common observation and accepted conclusion that gravity is conservative.  If gravity is not always conservative that needs to be proven.  That can be done by showing through repeatable and reliable experiment that gravity is not conservative under some set of conditions. 

I have taken your statements and attempted to express what I believe you hypothesize as at least one set of conditions where gravity is not conservative.  Please either confirm that those statements reproduced for your convenience here accurately represent your hypothesis, or change them as needed so that they do.  Then we can proceed to work on an experiment design to test the hypothesis.

1) The cycloid pendulum potential energy at its apogee contains only gravitational potential energy with all gravitational force operating normal to the horizon.
2) A circular path pendulum with a vertical length arm of y1 and bob mass m1 has at its apogee additional "third derivative energy" over and above the potential energy as an otherwise identical cycloid pendulum has.
3) A hybrid pendulum with vertical length arm of y1 and bob mass m1 that follows a circular path on one side of its travel and a cycloid path on the other half of its travel will convert the additional "third derivative energy" of the circular path half to additional gravitational potential energy observable as a higher apogee on the cycloid side than the circular side.