Re: [Phys-l] Sharing a problem for students

["Bob Sciamanda" <trebor@winbeam.com>]

Ludwik,
Fowles defines and investigates the stability of circular, central 
force orbits.  (Paragraph 6.13 of the 2nd edition).  He concludes that 
for power law central forces,  f(r)= -c*r^n,  circular orbits are 
stable if n > -3 .  Thus the inverse square law (n = -2) and the 
harmonic force law (n = 1) lead to stability.  Nowhere does he speak 
of  "dynamic" equilibrium/stability.

I don't see the "paradox" to which you refer.  Nor do I see the need 
for the adjective "dynamic".

You say, " The concept of  “dynamical equilibrium” was probably 
invented to describe
stability of orbits."  Where did you see this language invented/used?


Bob Sciamanda
Physics, Edinboro Univ of PA (Emeritus)
www.winbeam.com/~trebor
trebor@winbeam.com
----- Original Message ----- 
From: "Ludwik Kowalski" <kowalskil@mail.montclair.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, December 23, 2007 12:41 PM
Subject: Re: [Phys-l] Sharing a problem for students

. . .
> How to reconcile this undeniable fact
> with a statement that stability calls for a minimum of potential
> energy? A tiny change in r would not create a restoring force toward
> r=R. It would simply changes the orbit, from circular to elliptic. 
> The
> concept of “dynamical equilibrium” was probably invented to describe 
> >
> stability of orbits.  I have a heretical idea on how to reconcile the
> apparent paradox. But first I want to know what others think. I do 
> not
> to want to be embarrassed again. . . .