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Unified Mechanics Theory

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Introduction to Unified Mechanics Theory with Applications

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Abstract

The term unified is used to describe the unification of universal laws of motion of Newton and laws of thermodynamics ab initio level. As we discussed in earlier chapters, Newton’s laws do not account for energy loss or degradation. They only govern what happens to a system in the initial moment a load is applied to a brand-new structure. However, the laws of thermodynamics control what happens after the initial moment over time. Historically, continuum mechanics is based on the laws of Newton only, and phenomenological test data fit empirical models that are supposed to satisfy thermodynamics’ laws introduce energy loss, dissipation, and degradation. In the next section, we will discuss the earlier work on using thermodynamics in continuum mechanics.

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Notes

  1. 1.

    Translators’ footnote: The ambiguous symbol “l” [used by Boltzmann] for [natural] logarithm in the original text has been replaced throughout by “ln .”

  2. 2.

    Translators’ footnote: The original text reads as “maximized but should mean minimized” [because Boltzmann’s objective is to maximize P].

  3. 3.

    Boltzmann approximates ln x! by \( \left[x\ \ln x-x+\frac{1}{2}\ln \left(2\pi \right)\right] \) rather than \( \left[\left(x+\frac{1}{2}\right)\ln x-x+\frac{1}{2}\ln \left(2\pi \right)\right] \) as is now usual. For x ≫ 30,the relative difference is small.

  4. 4.

    Cardano’s formula.

  5. 5.

    Wien. Ber. (1875) 72:427–457 (Wiss. Abhand. Vol. II, reprint 32).

  6. 6.

    The quantity χ called “Kraftfunktion” or “Ergal” by Boltzmann is translated as potential energy.

  7. 7.

    Wien. Ber. (1875) 72:427–457.

  8. 8.

    Translators note: Altitude and azimuth?

  9. 9.

    Translator note: Here V should appear in the denominator, cf the equation after (4.165).

  10. 10.

    O. Lummer and E. Pringsheim, Transactions of the German Physical Society 2 (1900), p. 163.

  11. 11.

    H. Rubens and F. Kurlbaum, Proceedings of the Imperial Academy of Science, Berlin, October 25, 1900, p. 929.

  12. 12.

    H. Beckmann, Inaugural dissertation, Tübingen 1898. See also H. Rubens, Weid. Ann. 69 (1899), p. 582.

  13. 13.

    M. Planck, Ann. d. Phys. 1 (1900), p. 719.

  14. 14.

    Compare with Eq. (4.205).

  15. 15.

    M. Planck, loc. cit., pp. 730 ff.

  16. 16.

    Moreover one should compare the critiques previously made of this theorem by W. Wien (Report of the Paris Congress 2, 1900, p. 40) and by O. Lummer (loc. cit., 1900, p. 92).

  17. 17.

    L. Boltzmann, Proceedings of the Imperial Academy of Science, Vienna, (II) 76 (1877), p. 428.

  18. 18.

    Joh. v. Kries, The Principles of Probability Calculation (Freiburg, 1886), p. 36.

  19. 19.

    W. Wien, Proceedings of the Imperial Academy of Science, Berlin, February 9, 1893, p. 55.

  20. 20.

    M. Thiesen, Transactions of the German Physical Society 2 (1900), p. 66.

  21. 21.

    Perhaps one should speak more appropriately of a “white” radiation, to generalize what one already understands by total white light.

  22. 22.

    M. Planck, Ann. d. Phys. 1 (1900), p. 99.

  23. 23.

    F. Kurlbaum, Wied. Ann. 65 (1898), p. 759.

  24. 24.

    O. Lummer and E. Pringsheim, Transactions of the German Physical Society 2 (1900), p. 176.

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    Cemal Basaran

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Basaran, C. (2022). Unified Mechanics Theory. In: Introduction to Unified Mechanics Theory with Applications. Springer, Cham. https://doi.org/10.1007/978-3-031-18621-9_4

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