Re: [Phys-L] Help w/ Euler Cromer algo.
On 2014, Sep 20, , at 23:47, fletcher@physics.usyd.edu.au wrote:
> Hi Bernard
>
> This might help.
>
> https://www.siue.edu/~mnorton/mat-340.pdf
>
> Cheers
>
> Fletch
Thanks, but … curiously Cromer claims, additionally,*** that the half step is
not as good as the Last Point Approx., while the Garvin/Norton example is
rather convincing otherwise!
[maybe their criteria differ — reveals a lack of careful reading.]
What JD wrote is the "heart”.
On 2014, Sep 20, , at 22:18, John Denker <jsd@av8n.com> wrote:
> What is not claimed, and what is not generally true, is that
> the length of the simulated period will match the true period.
>
>> fitting the result to a cos
>
> That's asking too much. The simulated period will be off
> by a little bit, so the result will deviate from the exact
> cosine by an amount that grows over time.
>
> You could fudge the frequency of the cosine to alleviate
> this problem.
i.e. fit to the cos W/ a functional parameter to the frequency?
> Depending on the reason for doing the
> simulation, you might or might not care about the frequency
> discrepancy.
Great!
As usual, by being a telegrapher I failed to obtain a complete answer.
The “motivation” was to determine if a typical clock’s pendulum exhibited SHM.
[Of course it doesn’t, but to what degree? —]
IIUC, many horologists think it doesn’t (significantly — whatever that means)
One, using a Renishaw found it is SHM some time ago, but didn’t write it up, so
we don’t know w/ in what accuracy.
Hence the cos fit.
All this may be “moot”, as the deviation from “harmonicity” as measured by the
fit using the non-lin. diff. eq. [done after my post] “swamps” the inaccuracy
of the LPA by at least two orders!
I expect the fit of the diff. eq. including a drive numerically modeled will
result in further deviation.
One poss. prob. A not very gud mantel clock’s p.’s period on average over a
week deviates only ~ one PPM. This means that the horological definition of
harmonicity is in position only, not period. So “my” fit comparison must not
include variation of period.
***On 2014, Sep 20, , at 21:47, Bernard Cleyet <bernard@cleyet.org> wrote:
> Cromer claim(s) the Last Point approximation is stable. So I must not be
> writing it.
bc ’s next project: develop a sinusoidal fit w/ variable period. Yes?