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Archive for Rational Mechanics and Analysis

, Volume 70, Issue 4, pp 289–305 | Cite as

A mathematical theory of physical units, dimensions, and measures

  • Donald E. Carlson
Article

Keywords

Neural Network Complex System Nonlinear Dynamics Mathematical Theory Electromagnetism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Fourier, J., Théorie Analytique de la Chaleur. Paris: Didot 1822.Google Scholar
  2. Bridgman, P.W., Dimensional Analysis. New Haven: Yale University Press 1922.Google Scholar
  3. Langhaar, H.L., A summary of dimensional analysis. J. Franklin Inst. 242, 459–463 1946.Google Scholar
  4. Birkhoff, G., Hydrodynamics. Princeton: University Press 1950.Google Scholar
  5. Flieschmann, R., Die Struktur des physikalischen Begriffssystems. Z. Physik 129, 377–400 1951.Google Scholar
  6. Langhaar, H.L., Dimensional Analysis and Theory of Models. New York: John Wiley 1951.Google Scholar
  7. Flieschmann, R., Das physikalische Begriffssystem und die elektrischen Einheiten. Der mathematische und naturwissenschaftliche Unterricht 5, 130–140 1952/53.Google Scholar
  8. Drobot, S., On the foundations of dimensional analysis. Studia Mathematica 14, 84–99 1953.Google Scholar
  9. Fleischmann, R., Das physikalische Begriffssystem als mehr dimensionales Punktgitter. Z. Physik 138, 301–308 1954.Google Scholar
  10. Brand, L., The pi theorem of dimensional analysis. Arch. Rational Mech. Anal. 1, 35–45 1957.Google Scholar
  11. Fleischmann, R., Einheiteninvariante Größengleichungen, Dimensionen. Der mathematische und naturwissenschaftliche Unterricht 12, 385–399, 443–458 1959/60.Google Scholar
  12. Halmos, P.R., Naive Set Theory. Princeton: D. Van Nostrand 1960.Google Scholar
  13. Page, C.H., Physical entities and mathematical representation. J. Research Nat. Bureau Stds. 65B, 227–235 1961.Google Scholar
  14. Quade, W., Über die algebraische Struktur des Größenkalküls der Physik. Abh. Braunschweigischen Wiss. Ges. 13, 24–65. Translated as an appendix to Dimensional Analysis for Economists by F.J. De Jong. Amsterdam: North-Holland 1967 1961.Google Scholar
  15. Parkinson, M., An axiomatic approach to dimensions in physics. Am. J. Physics 32, 200–205 1964.Google Scholar
  16. Görtler, H., Die Grundlagen der Theorie der physikalischen Dimensionen. Z. angew. Math. Mech. 46, T3-T10 1966.Google Scholar
  17. Quade, W., Zur Theorie und Anwendung des Größenkalküls der Physik. Abh. Braunschweigischen Wiss. Ges. 18, 15–49 1966.Google Scholar
  18. Bunge, M., Foundations of Physics. Berlin-Heidelberg-New York: Springer 1967.Google Scholar
  19. Griesel, H., Algebra and Analysis der Größensysteme. Math.-Phys. Semesterberichte 16, 56–93, 189–224 1968.Google Scholar
  20. Whitney, H., The mathematics of physical quantities, Part I: Mathematical models for measurement. Am. Math. Monthly 75, 115–138 1968–1.Google Scholar
  21. Whitney, H., The mathematics of physical quantities, Part II: Quantity structures and dimensional analysis. Am. Math. Monthly 75, 227–256 1968–2.Google Scholar
  22. Bunge, M., A mathematical theory of the dimensions and units of physical quantities. In: Problems in the Foundations of Physics, edited by M. Bunge. Berlin-Heidelberg-New York: Springer 1971.Google Scholar
  23. Alten, H.W., & W. Quade, Analysis im Größenkalkül der Physik. Abh. Braunschweigischen Wiss. Ges. 23, 311–341 1971/72.Google Scholar
  24. Martinot-Lagarde, A., Classification des grandeurs scalaires. In: Symmetry, Similarity and Group Theoretic Methods in Mechanics, edited by P. G. Glockner & M. C. Singh. The University of Calgary 1974.Google Scholar
  25. Görtler, H., Dimensionsanalyse. Berlin-Heidelberg-New York: Springer 1975.Google Scholar
  26. Rychlewski, J., Mathematical foundations of the theory of dimensions, analogies and similarity. In: Trends in Applications of Pure Mathematics, edited by G. Fichera. London-San Francisco-Melbourne: Pitman 1976.Google Scholar
  27. Carlson, D.E., On some new results in dimensional analysis. Arch. Rational Mech. Anal. 68, 191–210 1978.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Donald E. Carlson
    • 1
  1. 1.Department of Theoretical and Applied MechanicsUniversity of IllinoisUrbana-Champaign

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