Abstract In Continuum Mechanics a widely cited formula, due to Nanson (Mess Math 7:182–185, 1878), contributes the relation between product of area and unit normal vectors relevant corresponding surfaces in two configurations 3D body. A geometric treatment provides equivalent expressions formula by direct elaborations on Euler – Jacobi volume change formula. Meaning limits are underlined. liter...

It is shown that the canonical balance of momentum of continuum mechanics can be formulated in a general way, but not independently of the usual balance of linear momentum, even in the absence of specified constitutive equations. A parallel construct can be made for the accompanying time-like canonical energy equation. On specifying the energy, previous particular cases can be deduced including...