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# Re: conservative forces +- non-dissipative forces

• From: "John S. Denker" <jsd@MONMOUTH.COM>
• Date: Sat, 30 Jun 2001 13:46:55 -0400

At 01:30 PM 6/30/01 -0400, I botched the end of my note:
Examples:
-- In an ideal roller-coaster, the track provides a force of constraint,
which is conservative (and therefore nondissipative).
-- In an undamped mass-on-a-spring oscillator, the spring provides a
force that is nondissipative, but not conservative.
-- A moving potential such as a catapult is non-conservative.
-- A charged particle in a changing magnetic field is subject to a
non-conservative force. The equation
V = phi dot
is a law of nature. The corresponding force is not the gradient of any
potential. It is not dissipative.
-- Any dissipative process is necessarily non-conservative.

Sorry. I should have said:

Examples:
-- In an ideal roller-coaster, the track provides a force of constraint,
which is conservative (and therefore nondissipative). Indeed it does no
work whatsoever.
-- In an undamped mass-on-a-spring oscillator, the spring does nonzero
work on the mass, but the force is conservative (and therefore
nondissipative) because the whenever the system coordinate (the
displacement) returns to its original value, the energy in the spring is
the same.
-- If you run up the escalator and then run down the stairs, you have
returned yourself to the initial coordinate but you have _not_ returned the
escalator to its original energy state, even if we neglect
dissipation. This is very different from running up and down the stairs,
which (in the absence of dissipation) would be conservative.
-- A catapult is non-conservative.
-- In general, a moving potential is non-conservative.
-- A charged particle in a changing magnetic field is subject to a
non-conservative force. The equation
V = phi dot
is a law of nature. The corresponding force is not the gradient of any
potential. It is not dissipative.
-- Any dissipative process is presumably non-conservative.