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In a series of previous articles by the author, it was shown that one couldeffectively give a variational formulation to non-conservative mechanicalsystems, as well as ones that subject to non-holonomic constraints by startingwith the virtual work functional instead of an action functional. In thisarticle, it is shown that when one starts with a virtual work functional thatis not exact, so it does not admit an action functional, instead ofconservation laws the extension of Noether's theorem gives balance principlesfor non-conserved currents. Examples of this generalized Noether identity aregiven in the mechanics of points, rigid bodies, and deformable bodies.

A generalization of Noether's theorem based on the virtual work functional