
Classical Mechanics40
© 2010 Taylor & Francis Group, LLC
The line integral for the work then becomes independent of the path of integration and depends only
on the initial and nal positions of the particle:
WFrV
A
B
A
B
=⋅=−
dd
(2.29)
where V
A
is the potential energy of the particle at point A, similarly to V
B
.
Forces whose work is independent of the path are called conservative forces, and the motion
under the action of such forces is known as conservative motion. Equation 2.28 is the necessary
condition for a conservative force that is a function of position. It can be shown that it is also a suf-
cient condition. From Equation 2.28, w