Re: [Phys-l] Classical Adiabatic Invariant

[John Denker <jsd@av8n.com>]

On 06/06/2011 10:53 AM, Bernard Cleyet wrote:
> I'm attempting to understand this as applied to a simple pendulum.
> The examples I've  found apply to shortening the rod.  Wherein
> E/omega is a constant.  Shortening the rod increases the frequency,
> so the E must increase.

On 06/06/2011 06:26 PM, we got a clarification:
> > The changes are very slow.  i.e.   The increase  of v. ~ 60
> > microgals, (in ~9.8E+8micro. ) which "takes" ~12 hours.  The period
> > of the pendulum is 2Hz.

In the limit of very slow changes, this is an easy problem.
It involves nothing more than high-school physics.

If you approach it the right way, you should be able to do
it in your head, in less time than it takes to tell about it.

Hint:  The energy is *not* proportional to omega.

Bigger hint:  There are some classical invariants that can 
be invoked.  E/omega is just not one of them.

Ginormous hint:
Ercynpr gur ebq ol n fgevat gung cnffrf guebhtu n ubyr va 
na vzzbinoyr gbc-cyngr.  Chyyvat ba gur fgevat unf gur fnzr 
arg rssrpg nf fubegravat gur ebq ... ohg vg znl or rnfvre 
gb nppbhag sbe gur sbepr ba gur fgevat.