Re: [Phys-L] adiabatic invariance confusion

[Bernard Cleyet <bernard@cleyet.org>]

Brian!

Thanks for your reply, however …….

On 2014, Feb 28, , at 07:18, brian whatcott <betwys1@sbcglobal.net> wrote:

> It seems fanciful to suppose that a fixed solenoid interacting with a swinging button magnet
> models a force due to gravity at all accurately.

Co-linearly, IIRC, the (dipole-dipole) interaction is 1/R^3.  Off axis much “worse”   I only call it pseudo-g for simplicity.  Whatever;  it changes the restoring force and, therefore, a change in the numerator parameter of the coefficient.  [g/l]



> Supposing the solenoid imposed an extremely strong  magnetic field, the button magnet swinging in its vicinity would likely be immediately captured which I think you are equating to a high value of g.

Captured not, essentially, no different from the capture of a pendulum by the earth’s g



> It seems to me that the force imposed upon the pendulum represents work done and so claiming adiabasis seems  problematical.

That’s the major prob. I have.  How is this different from shortening the rod (as done in an AJP article***), and Eherenfest’s “Gedankenexperiment”, or tilting the plane of motion, as reported severally. If I weren’t so maths. declined, I’d see why the “H" is constant.  


> Perhaps a very slow change in effective pendulum length - using pendulum bob or pivot point displacement might meet your needs better?  

Not "really”.  I didn’t want a “better” experiment (don’t think I can afford it, and, besides, already done.); I wanted an explanation for why a change in the “effective” and average g in ~ one period is so different from over many periods.  
i.e. product ~ constant and not.

***  Wrong! it’s Eur. J. of Phys.  [Theorie und Praxis]  :

"A Hamiltonian approach to the parametric excitation …"


Index of /adiabatic  

http://www.cleyet.org/adiabatic/

‎www.cleyet.org/adiabatic/A%20Hamiltonian%20approach%20to%20the%20parametric%20excitation%200143-0807_27_3_001.pdf

bc, as a result of re-skimming the article will try an undriven v. high Q pendulum with a pseudo-g change.

> Brian Whatcott    Altus OK
>
> On 2/28/2014 1:47 AM, Bernard Cleyet wrote:
> > Showing an adiabatic invariance with a macroscopic harmonic oscillator is v. difficult, because of dissipation.  For another reason I’ve been changing the effective g of an E-M clock driven pendulum.  The magnet attached to the bottom of the bob completes the clock drive and serves to change the effective g using a solenoid waxed beneath the sense and drive coils of the Fedchenko type drive.  After many trials, I thought, perhaps a driven pendulum WRT adiabatic invariance would be the same as a dissipation-less pendulum.  So I tried changing the “g” using an RC supply to the solenoid (L ~ 190 mH)  The measured TC is ~ 93s   (R ~ 2K Ohm; C ~ 16K microFd calc’d 32s).  Nada!  Tho the g increase is ~ 35% (TC ~ 96s and the period is ~ 1s)  By a stroke of luck I thought, well, how about the extreme of my previous trials (TC < 1s!).  Wow!  The product Omega * Amplitude is the same once equilibrium obtained.   (W/ and W/O the added g  within ~ 1/2%)  While the ”supposedly" adiabatic trial has a difference of ~ 5%
> >
> > “What gives?”
> >
> > bc theory, etc. declined.