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The Comparison Method of Physical Quantity Dimensionalities

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Computer Algebra in Scientific Computing (CASC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5743))

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Abstract

There is examined the comparison method of dimensionalities on a basis of group-theoretical analysis. It has obtained certain scaling group and operators possible within the differential equations for different tasks. It has made the comparison of calculated operators of tension with known results.

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References

  1. Birkhoff, G.: Dimensional analysis of partial differential equations. J. Electr. Engng. 67, 1185–1188 (1948)

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  2. Buckingham, E.: Model experiments and the forms of empirical equations. Trans. Amer. Soc. Mech. Eng. 37, 263–296 (1915)

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  3. Ovsyannikov, L.V.: Group Analysis of Differential Equations. Nauka, Moscow (1978) (in Russian)

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  4. Olver, P.J.: Applications of Lie Groups to Differential Equations. Springer, New York (1986)

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  5. Marusina, M.J., Flegontov, A.V.: Applications in mechanics of the dimensionalities theory and groups theory. Scientific Instrument Making 15(1), 94–99 (2005)

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Author information

Authors and Affiliations

  1. Herzen State Pedagogical University of Russia, 48, Moika Emb., 191186, St.-Petersburg, Russia

    Alexander V. Flegontov

  2. St.Petersburg State University of Information Technology, Mechanics and Optics, Russia

    M. J. Marusina

Authors
  1. Alexander V. Flegontov
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  2. M. J. Marusina
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Editor information

Editors and Affiliations

  1. Joint Institute for Nuclear Research, Laboratory of Information Technologies, Dubna, Russia

    Vladimir P. Gerdt

  2. Technische Universität München‘, Institut für Informatik, Garching, Germany

    Ernst W. Mayr

  3. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2009 Springer-Verlag Berlin Heidelberg

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Flegontov, A.V., Marusina, M.J. (2009). The Comparison Method of Physical Quantity Dimensionalities. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2009. Lecture Notes in Computer Science, vol 5743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04103-7_8

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  • DOI: https://doi.org/10.1007/978-3-642-04103-7_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04102-0

  • Online ISBN: 978-3-642-04103-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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