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-- 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.