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

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

2011-09-02

arxiv.org/abs/1109.0461v1

Physics

Mathematical Physics

30 pages

Scientific paper

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.

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