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


Abstract
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.

Keywords:
conservation laws, vector-valued forms, reference frames

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