Godunov Methods pp 399-410 | Cite as

# Thermodynamics, Conservation Laws and their Rotation Invariance

Chapter

## Abstract

Late in the 1950s, when I developed methods of gasdynamics computations, I, being under the influence of variational principles, arrive at a conclusion that the equations of gasdynamics belong to the class of equations of the following form:
On smooth solutions to these equations, one more additional relation holds:
In fact, this relation is a thermodynamic identity.

$$
\frac{{\partial {L_{qi}}}}{{\partial t}} + \frac{{\partial M_{{q_i}}^j}}{{\partial {x_j}}} = 0.
$$

(1)

$$
\frac{{\partial \left( {{q_i}{L_{qi}} - L} \right)}}{{\partial t}} + \frac{{\partial \left( {{q_i}M_{{q_i}}^j - {M^j}} \right)}}{{\partial {x_j}}} = 0.
$$

(2)

## Keywords

Irreducible Representation Thermodynamic Potential Rotation Group Additional Relation Harmonic Polynomial
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## References

- 1.Godunov S. K. (1960) On the concept of generalized solution.
*Soviet. Math. Dokl*, Vol. 1, pp. 1194–1196, 1960.MathSciNetMATHGoogle Scholar - 2.Godunov S. K. and Romenskii E. I. (1998) Elements of Continuous Media and Conservation Laws.
*Universitetskaya Seriya*. Vol. 4. Scientific Books Publisher. Novosibirsk.1998 [in Russian].Google Scholar - 3.Godunov S. K., Romenskii E. I., and Mihailova T. Yu. (1996) Systems of thermody-namically coordinated laws of conservation invariant under rotations.
*Siberian Math.J.*Vol. 37.**4**.pp. 690–705. 1996.MathSciNetMATHCrossRefGoogle Scholar - 4.Mihailova T. Yu. (1997) Thermodynamically coordinated laws of conservation with unknowns of arbitrary weight.
*Siberian Math. J.*Vol. 38.**3**. 1997.MathSciNetGoogle Scholar - 5.Godunov S. K. and Mihailova T. Yu. (1998) Representation of the Rotation Groups and Spherical Functions.
*Universitetskaya Seriya*. Vol. 3. Scientific Books Publisher.Novosibirsk. 1998 [in Russian].Google Scholar

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© Springer Science+Business Media New York 2001