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Re: [Phys-l] Simulating a disturbance of a stable planetary system.



On 01/01/2008 02:52 PM, chuck britton wrote:
Use the analogy of the 'cone' lying on its side.
This a mechanically 'Neutral Equilibrium'.

Not 'Stable' (self correcting) Disturbance => Return to Initial
Condition.

Nor 'Unstable' Disturbance => disaster

But' Neutral'
Disturbance => moves to (most likely) New, Different condition of
equilibrium.

Circles and ellipses are both neutral equilibrium conditions.
Each disturbance shifts the system to different (but still neutrally
stable) equilibrium.

All true. These are the well-established definitions. Things
are defined that way for good reasons, very good reasons, and
the definitions are not going to change anytime soon.

In any case, arguing about terminology is not an acceptable
substitute for understanding the physics. The physics underlying
this thread is perfectly clear.

Confusion comes from naming the 'cone standing upright' as Stable
while naming the lying down on its side as being 'Neutrally Stable'

To help prevent confusion, I emphasize the term "zero stability"
as a synonym for neutral stability.

Also:
→ A system with zero stability is neither stable or unstable.
→ A system with zero stability is both neutrally stable and neutrally unstable.

=================

More generally, the name of a thing is not a description of
the thing! Neutral stability is not stability. Chocolate
turtles are not made from turtles. Milk of magnesia is not
made from milk. A horse chestnut is not the same as a
chestnut horse. The Holy Roman Empire was neither holy,
nor Roman, nor an empire.

Perhaps we need a pedagogical adjective to describe the 'Standing
Upright' stability as maybe 'Self-Correcting Stability'

That's called stability. If you really need an adjective, call
it strict stability ... but you're better off without the adjective.

as opposed to
'Go-with-the-Flow (neutral) Stability.

That's called neutral stability or zero stability.

BTW this brings into play notions of /continuity/ i.e. bounded
response to a bounded disturbance.

A stable system always exhibits bounded response to a bounded
disturbance, but the converse does not hold. If you see a
bounded response, that does not prove that the system is
stable.

I think that PC (Pedagogically Correct) semantics
is a big part of this current discussion.

I disagree.

Arguing about definitions is characteristic of scholasticism,
which is not PC. It went out of fashion several hundred years ago.

First of all, from the pedagogical point of view *and* from the
physics point of view, it is preferable to describe how the system
behaves. Several people have done this, describing the behavior
in terms of objective, observable physics ... but evidently not
everyone has gotten the message.

Secondly, much of the discussion has suffered from assuming that
the system was "stable" according to one misdefinition, and then
assuming that it would behave as "stable" according to some other
misdefinition. This is not what I would call pedagogically
correct. It's not good pedagogy. It's not good science. It's
not even good scholasticism.

BTW I am aware that some "authorities" e.g. Arons (1996) advocate
(and practice) giving multiple inconsistent definitions to a given
technical term, and switching from one meaning to another on a
whim. If you want to know what I think of this, see:
http://www.infoplease.com/thesaurus?word=bad