Re: [Phys-L] Help w/ Euler Cromer algo.
BC:
I'm trying to reproduce your original problem and am finding that the residual
(thetamax*cos(wt)-theta_calculated(t)) depends on thetamax. What was your
theta max to get such small residuals (~e-9)? If I use a thetamax of 0.1
radians, I get a maximum residual of about 3.1*e-4 over 5 periods and it
doesn't grow quickly. That's with 1 ms time step. When I cut the time to 0.1
ms, the residual drops to 3.1*e-5. That's a first order effect which is what I
would expect. My residual is not growing quickly. It grows from 3 to 3.7
(*e-4) over 50 periods. At 100 periods (100,000 time steps) it's barely over 4.
I'm using iPython notebook to compute this. Looks pretty stable to me.
-> -----Original Message-----
-> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of
-> Bernard Cleyet
-> Sent: Sunday, September 21, 2014 12:58 PM
-> To: Forum Physics Educators
-> Subject: 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?
->
->
->
->
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