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Balance Equations in Skew Curvilinear Coordinate Systems

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An Expedition to Continuum Theory

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 210))

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Abstract

We now return to the balances of Chap. 3 and rewrite them for arbitrary coordinate systems. We start with the balances in regular points and, in this context, with the simplest one, namely the balance of mass, which is a scalar equation. We then move on to the more complex ones for momentum, energy, as well as total angular momentum, and specify them for cylindrical and spherical coordinates. As before we follow both ways and present the balances in index form as well as symbolically. The chapter ends with a discussion of the jump conditions and of global balances in arbitrary coordinates.

There are two sides of the balance sheet—the left side and the right side.

On the left side, nothing is right, and on the right side, nothing is left !

Answer by UBS to the journalist Dirk Maxeiner after the resignation of Ingrid Matthäus-Maier, CEO of KfW Bank

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References

  1. Chandrasekhar S (1981) Hydrodynamic and hydromagnetic stability. Dover Publications Inc, New York

    Google Scholar 

  2. Greve R (2003) Kontinuumsmechanik—Ein Grundkurs für Ingenieure und Physiker. Springer, Berlin

    MATH  Google Scholar 

  3. Haupt P (2002) Continuum mechanics and theory of materials, 2nd edn. Springer, Berlin

    Book  MATH  Google Scholar 

  4. Irgens F (2008) Continuum mechanics. Springer, Berlin

    Google Scholar 

  5. Landau LD, Lifschitz EM (1987) Fluid mechanics. Course of theoretical physics, vol 6, 2nd edn. Butterworth-Heinemann

    Google Scholar 

  6. Moeckel GP (1974) Thermodynamics of an interface. ARMA 57:255–280

    Article  MathSciNet  Google Scholar 

  7. Müller I (1985) Thermodynamics. Pitman Advanced Publishing Program, Boston

    MATH  Google Scholar 

  8. Özişik MN (1989) Boundary value problems of heat conduction. Dover Publications Inc, Mineola

    Google Scholar 

  9. Segel LA (1987) Mathematics applied to continuum mechanics. Dover Publications Inc, Mineola

    Google Scholar 

  10. Sokolnikoff IS (1956) Mathematical theory of elasticity. McGraw-Hill Book Company Inc, New York

    MATH  Google Scholar 

  11. Truesdell C, Toupin R (1960) The classical field theories. In: Flügge S (ed) Encyclopedia of physics. Volume III/1 Principles of classical mechanics and field theory. Springer, Berlin

    Google Scholar 

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Correspondence to Wolfgang H. Müller .

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Müller, W.H. (2014). Balance Equations in Skew Curvilinear Coordinate Systems. In: An Expedition to Continuum Theory. Solid Mechanics and Its Applications, vol 210. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7799-6_5

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  • DOI: https://doi.org/10.1007/978-94-007-7799-6_5

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-7798-9

  • Online ISBN: 978-94-007-7799-6

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