On 05/18/2003 08:30 PM, Carl Mungan wrote:
[non-dissipative, allegedly non-conservative forces]
>>> examples: static friction, tension exerted by
>>> nonstretching strings, etc.
I wrote:
>> -- Dissipation has to do with a change in entropy.
>
> Okay.
>
>> -- Non-conservative force has to do with a change in energy.
>
> This seems a bit too vague to me: exactly what kind of energy do you
> mean? energy of what, the agent or the object?
Well, consider a betatron. The electron goes
around one loop. The object (electron) gains
energy. The agent (betatron hardware) loses
energy. Energy is not a function of position;
it depends on the path.
> since "change" can be
> either an increase or decrease, it seems to me that lack of change is
> also permitted, yes?
If we go around a closed loop and the energy change
is provably zero, I want to call it conservative.
I don't see any reason not to.
> Conservative forces can store up energy in
> potential form;
They store it only temporarily. The accumulation
around a closed path is zero.
> nonconservative forces do not,
Why not? Suppose I operate a betatron backwards,
so that energy is transferred from the electron
to PE in the betatron hardware. That seems like
nonconservative energy storage to me.
> but I don't see that
> requires a loss/gain of energy. I'm reluctant to take a Coriolis
> force to be conservative.
>
>> The force is not a function of position.
>
> I would like to add this as a requirement for a force to be
> conservative.
Well, Carl is consistent in his terminology.
Other folks use different terminology.
An ideal swing-set (with non-stretchy strings,
stationary pivot, no friction) is a fine
example of a force of constraint. There
can be no exchange of energy between the
swinger and the earth. So it is conventional
to call this a conservative system. The
force is not a function of position alone.
I don't see what's to be gained by declining
to call this conservative. In my book it
is nondissipative but conservative.
It's a holonomic constraint on the position
and a holonomic constraint on the energy, but
it is not a holonomic constraint on the force.