Geodesic
Geometric formulations of the balance laws of continuum mechanics
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 150-176

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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. 
@article{DVMG_2018_18_2_a2,
     author = {A. I. Gudimenko},
     title = {Geometric formulations of the balance laws of continuum mechanics},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {150--176},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a2/}
}
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A. I. Gudimenko. Geometric formulations of the balance laws of continuum mechanics. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 150-176. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a2/