Material Symmetry and Conservation Laws

The balance of material momentum, also known as impulse or pseudomomentum, is an important concept in continuum mechanics whose significance and utility is not always apparent. For certain simple systems, this balance can also be derived as the projection of the linear momentum balance onto the material manifold. We will discuss this balance law and its association with the material symmetry of purely mechanical systems governed by an action. We will explore the implications of this concept in various areas, including the classification of planar rods, solution of partial constraint problems, and derivation of conserved quantities in ideal fluids.