  In a series of previous articles by the author, it was shown that one could
effectively give a variational formulation to non-conservative mechanical
systems, as well as ones that subject to non-holonomic constraints by starting
with the virtual work functional instead of an action functional. In this
article, it is shown that when one starts with a virtual work functional that
is not exact, so it does not admit an action functional, instead of
conservation laws the extension of Noether's theorem gives balance principles
for non-conserved currents. Examples of this generalized Noether identity are
given in the mechanics of points, rigid bodies, and deformable bodies.
