Geodesic
Geometrical aspects of the mass conservation law
Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 2, pp. 173-190.

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The theory of fiber bundles is used for representation of the mass conservation law in a coordinate-free form. А generalized formulation of the law is proposed and its physical interpretations are discussed. 
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A. I. Gudimenko; M. A. Guzev. Geometrical aspects of the mass conservation law. Dalʹnevostočnyj matematičeskij žurnal, Tome 14 (2014) no. 2, pp. 173-190. http://geodesic.mathdoc.fr/item/DVMG_2014_14_2_a4/

[1] F. Klein, Lektsii o razvitii matematiki v XIX stoletii, ONTI, M.–L., 1998

[2] A. Puankare, O nauke, Nauka, M., 1990 | MR

[3] L. I. Sedov, “Matematicheskie metody postroeniya novykh modelei sploshnykh sred”, UMN, 20:5(125) (1965), 121–180 | MR | Zbl

[4] G. Romano, R. Barretta, M. Diaco, “Geometric continuum mechanics”, Meccanica, 49:1 (2014), 111–133 | DOI | MR | Zbl

[5] S. K. Godunov, E. I. Romenskii, Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Nauchnaya kniga, Novosibirsk, 1998

[6] L. I. Sedov, Mekhanika sploshnoi sredy, T. 1, Nauka, M., 1994 | MR

[7] D. Saunders, The Geometry of Jet Bundles, Cambridge Univ. Press, Cambridge, 1989 | MR | Zbl

[8] J. Ehlers, “The Nature and Structure of Space-Time”, The Physicist$^\prime$s Conception of Nature, ed. J. Mehra, Raidel, Dordrecht, 1973, 71–91 | DOI

[9] E. Cartan, “Sur les variétés à connexion affine et la théorie de la relativité généralisée (premiére partie)”, Ann École Norm Sup., 40 (1923), 325–412 | MR

[10] E. Cartan, “Sur les variétés à connexion affine et la théorie de la relativité généralisée (suite)”, Ann École Norm Sup., 41 (1924), 1–25 | MR

[11] A. Bernal, M. Sanchez, “Leibnizian, Galilean and Newtonian structures of space-time”, J. Math. Phys., 44 (2003), 77–108 | DOI | MR

[12] A. Trautman, “Foundations and current problems of general relativity”, Lectures on General Relativity. Volume 1 of Brandeis Summer Institute in Theoretical Physics, ed. S. Deser and K. Ford, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965, 1–248

[13] A. Trautman, “Fibre Bundles Associated with Space-Time”, Reports in Mathematical Physics, 1 (1970), 29–62 | DOI | MR | Zbl

[14] A. Trautman, “A classification of space-time structures”, Reports in Mathematical Physics, 10 (1976), 297–310 | DOI | MR | Zbl

[15] G. Giachetta, L. Mangiarotti and G. Sardanashvily, Geometric formulation of classical and quantum mechanics, World Scientific, Singapore, 2011 | MR | Zbl

[16] S. P. Novikov, I. A. Taimanov, Sovremennye geometricheskie struktury i polya, MTsNMO, M., 2005

[17] F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, Berlin, 1983 | MR | Zbl

[18] A. Jadczyk, M. Modugno, Galilei general relativistic quantum mechanics, Report of Department of Applied Mathematics, University of Florence, 1994 http://www.dma.unifi.it/~modugno/

[19] W. Noll, “On the continuity of the solid and fluid states”, J. Rational Mech.Anal., 4 (1955), 3–81 | MR | Zbl

[20] C. Truesdell, R. Toupin, “The classical field theories”, Encyclopedia of Physics, ed. S. Flugge, Springer-Verlag, Berlin, Gottingen, Heidelberg, 1960 | MR | Zbl

[21] J. Koszull, Lectures on fibre bundles and differential geometry, Notes by S. Ramanan, Tata Institute of Fundamental Research, Bombay, 1960 | MR

[22] G. Giachetta, L. Mangiarotti and G. Sardanashvily, Advanced Classical Field Theory, World Scientific, Singapore, 2009 | MR | Zbl

[23] I. Kolár, P. Michor, J. Slovák, Natural operations in differential geometry, Springer-Verlag, Berlin, Heidelberg, New York, 1993 | MR

[24] B. Schutz, Geometrical methods of mathematical physics, Cambridge Univ. Press, Cambridge, 1980 | Zbl

[25] L. D. Landau, E. M. Lifshits, Teoreticheskaya fizika. T. VI. Gidrodinamika, Fizmatlit, M., 2001