Geometric formulations of the balance laws of continuum mechanics
A. I. Gudimenkoab
a Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok
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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MSC: Primary 74A05; Secondary 53B50
A. I. Gudimenko, “Geometric formulations of the balance laws of continuum mechanics”, Dal'nevost. Mat. Zh., 18:2 (2018), 150–176
Citation in format AMSBIB
\paper Geometric formulations of the balance laws of continuum mechanics
\jour Dal'nevost. Mat. Zh.
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