Far Eastern Mathematical Journal

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Geometric formulations of the balance laws of continuum mechanics

Gudimenko A.I.

2018, issue 2, Ñ. 150-176

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.

conservation laws, vector-valued forms, reference frames

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