Impulse and material symmetry

The balance of material momentum, also known as impulse or pseudomomentum, arises from material (relabeling) symmetry. We will present a brief overview of the history of this balance law of continuum mechanics, and discuss it in the context of an ideal fluid. It will be shown that Kelvin’s circulation theorem, Cauchy’s invariants, Weber’s integral, and other related quantities follow from this balance law, as do correspondences between seemingly disparate concepts such as circulation and the J-integral of fracture mechanics.