Geometric formulations of the balance laws of continuum mechanics

The balance laws of classical continuum mechanics are formulated in terms of differential forms (mass balance) and vector-valued differential forms (balances of momentum and energy) on the trajectory of material continuum. The traditional formulations of the laws are obtained as a consequence of the proposed formulations. Balance equations are written in a form suitable for an arbitrary observer. The formulation of the equation of motion of an ideal fluid in terms of differential forms is derived from the proposed formulations.