Sorry, my obscene post was not nice.

But the aloof and arrogant reasoning of Grimer made me respond with something as absurd as his arguments. Not everybody saw the joke, again sorry.

Please read this document carefully http://www.antique-horology.org/piggott/rh/images/81v_cycloid.pdf (posted by Grimer http://www.overunity.com/13480/big-try-at-gravity-wheel/msg383571/#msg383571).

The document says that the "chops" do not cause a true cycloid pendulum movement (or a isochronous clock) and that they were abandoned by the clock builders quite soon for this reason.

So, as I said, there is no way of causing a cycloid pendulum movement with gravity alone (by adding some guides or chops).

Greetings, Conrad

Correct. Your obscene post was not nice. But since you've apologised we'll move on.


I looked again at the link I gave and found the there are no less that 60 references to "chops".


For your penance ;-) and to save me having to trawl through all 60 please could you tell me which reference to chops you are referring to.


Thank you.


Edit: I have now searched on the word "true" and it comes up with a much smaller number of hits.


I think quote on page 15 may be the one you are referring to.

But he deduced something else as well. When the work on the rigid body pendulum was published in Part
IV of Horologium Oscillatorium, Huygens put it unequivocally, at Proposition XXIV, “It is not possible to
determine the centre of oscillation for pendula suspended between cycloids.” The very reason this is true
means that cycloidal chops do not provide an isochronous path for a rigid body pendulum.

But as you can see from the diagram on page 15 below the above quote this is not the kind of pendulum we
are discussing here.


Wouldn't you agree?

I looked again at the link I gave and found the there are no less that 60 references to "chops".

For your penance ;-) and to save me having to trawl through all 60 please could you tell me which reference to chops you are referring to.

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

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.

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.

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.

I've just seen something.


There's a James Burke connection between the Brachistochrone[/font][/size] and the graph below.


More tomorrow.



Brachistochrone[ bruh-kis-tuh-krohn]

noun [Mechanics]


1.
the curve between two points that in the shortest time by abody moving under an external force without friction; the curve of quickest descent.

http://en.wikipedia.org/wiki/Tautochrone_curve

http://en.wikipedia.org/wiki/Brachistochrone_curve

Good addition to the armoury.


Thanks, Fletch.