On 05/17/2003 08:32 PM, Carl Mungan wrote:
> ... I would link the idea of "conservative" to
> "existence of a potential"
Yes, for forces that are a function of position.
> as tested by "curl of force is zero"
Yes, for forces that are a function of position.
> or less formally, "work is path independent."
I would argue that that is more formal and more
general than the previous versions. See below.
> With this definition, it
> is important to realize that a force can be nonconservative without
> being dissipative -
Yes.
> examples: static friction, tension exerted by
> nonstretching strings, etc.
Whoa, lost me there.
1) Nonstretching spring = contradiction in terms.
2) I don't see how static friction can be a force FIELD
so therefore the question of whether it is derived
from a potential is unaskable. I don't see how the
work can be a function of path (or the opposite) if
there are no paths (because things are static).
4) To enlarge the discussion, consider Coriolis
forces. They are a function of velocity, not a
function of position. They are manifestly not
the gradient of any potential. But they contribute
zero work to the particle, regardless of path, so
their work is path-independent. I consider them
conservative for this reason.
> ... in my view
> almost all forces are nonconservative. The *only* common exceptions
> are gravitational, Hookean spring, and electrostatic forces.
Nonlinear springs are commonly nondissipative
and indeed conservative (to an excellent approximation).
Magnetostatics is also nondissipative and indeed
conservative.
The work done by a moving constraint is typically
nondissipative but not conservative ... in
contrast to a stationary constraint which is
conservative. Example: with a slight idealization
you can imagine an _elastic_ collision between a
baseball and a bat. That is nondissipative but
highly nonconservative in the lab frame.