Big try at gravity wheel

[Grimer]

In this document (which was cited by you) http://www.antique-horology.org/piggott/rh/images/81v_cycloid.pdf they talk about chops in old pendulum clocks which were supposed to cause cycloid pendulum movement but they did not. Therefore the clock builders abandoned chops and the idea of an isochronous clock.

"It is said that Huygens deduced that, if the chops were cycloidal, the bob of a pendulum would swing
along a cycloidal path, rather than the circular arc of the simple pendulum, and the pendulum would then
be isochronous."

My argument: there is no way to cause a pendulum weight to go along a cycloid path by gravity alone. No "chops" or any other "guides" can do that. One needs to introduce other forces provided by some additional mechanisms (which will consume energy and the consumed energy will be at least the energy gained by the cycloid path, if there is indeed some energy gained).

But my heart is not in "gravity machines", therefore I will not invest more time in this topic. I belive in experiments, theory is cheap.

Good science is derived from experiments. Every valid theory must be supported by real experiments. Of course you may decline experiments, but that will also decline your credibility. But again, count me out, I am interested in other strange things.

Greetings, Conrad

A very sensible decision. Good luck with your experiments.

[MarkE]

Grimer, it is looking more and more like you will not confirm or correct my statement of your hypothesis.  If that is the case then I'll do what I can to resolve the hypothesis as stated.  My strong suspicion is that the hypothesis as stated is falsifiable on its face using existing experiment data.  If my statement of your hypothesis is not accurate, it would therefore be to your advantage to post a correct statement of your hypothesis.

[Grimer]

Grimer, it is looking more and more like you will not confirm or correct my statement of your hypothesis.  If that is the case then I'll do what I can to resolve the hypothesis as stated.  My strong suspicion is that the hypothesis as stated is falsifiable on its face using existing experiment data.  If my statement of your hypothesis is not accurate, it would therefore be to your advantage to post a correct statement of your hypothesis.

The 2nd order derivatives are the same but the 3rd order derivatives are not.


If the problem were easy it would have been solved before, wouldn't it.

[MarkE]

The 2nd order derivatives are the same but the 3rd order derivatives are not.


If the problem were easy it would have been solved before, wouldn't it.

Grimer, there aren't that many options:  One is write down your hypothesis, and another is to keep avoiding it.  You can confirm my statement of your hypothesis that I faithfully derived from your stated comments, or if I didn't get it right simply state your hypothesis.  A third alternative is that you don't have a hypothesis.  That's OK too.  If that's the case, just say so.

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.

[Grimer]

Mark


Why is the Brachisochrone path the shortest time of descent?


Why does any other path take longer?


Isn't it reasonable that going down some other path is going to leave its mark, its fingerprint.


If you only measure the 2nd derivative you won't be capable of saying down which path the
bob has come.


But if in addition you measure the 3rd derivative you will.


The paths are different, the third derivatives are different but not the second.


Newtonian Gravity is the same (2nd derv) but not Ersatz Gravity (3rd derivative).


You are concentrating on NG and forgetting about EG.


I PMed you about EG. I assume you got it.