Balance Equations

Borrowing from the mechanics of systems of particles, the balance equations for mass, linear momentum, and angular momentum are established. Next, the balance of energy is obtained after having realized that energy in general requires a more general framework including quantities of non-mechanical character. The balance of entropy is made formal by assuming that the entropy rate, deprived of the divergence of an entropy flux and of an entropy supply, is non-negative. Next, balance equations are established for electromagnetism in deformable bodies. Jump relations are derived for balance properties across singular surfaces.