Advertisement

Mathematical modeling and dimensional analysis

An application to four-wheel steering
  • J. Molenaar
Part of the Mathematics and Its Applications book series (MAIA, volume 81)

Abstract

We present in §2 a general introduction on mathematical modeling. Irrespective of the case under consideration, the process of mathematical modeling has a general structure. See also references [1,–,6]. This structure comprises a sequence of stages followed again and again. An important ingredient of the modeling process is dimensional analysis . In §3 the main ideas of this technique are presented.

Keywords

Froude Number Dimensional Analysis Global Attractor Dimensionless Quantity Front Wheel 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

On mathematical modeling

  1. 1.
    F.A.Bender An Introduction to Mathematical Modeling John Wiley & Sons, New York, 1978, ISBN 0-471-02951-3.Google Scholar
  2. 2.
    J.S.Berry D.N.Burghes I.D.Huntley (eds.), Teaching and Applying Mathematical Models Ellis Horwood, Chichester, 1985, ISBN 085312-728-X.Google Scholar
  3. 3.
    D.N.Burghes M.S.Borrie ,Chichester, Ellis Horwood, 1981.Google Scholar
  4. 4.
    R.R.Clements Mathematical Modeling a Case Study Approach Cambridge University Press, 1989, ISBN 0-521-34340-2.CrossRefGoogle Scholar
  5. 5.
    D.W.Jordan P.Smith , Non-linear Ordinary Differential Equations Oxford University Press, 1977, (*).Google Scholar

On dimensional analysis

  1. 6.
    A.B.Tayler Mathematical Models in Applied Mechanics Clarendon Press, Oxford, 1986, ISBN 0-19-853533-3.zbMATHGoogle Scholar
  2. 7.
    G.I.Barenblatt Similarity Self-Similarity and Intermediate Asymptotics Consultants Bureau, New York, 1979, ISBN 0-306-10956-5.Google Scholar
  3. 8.
    E.A.Bender see [1].Google Scholar

On similarity solutions

  1. 9.
    G.I.Barenblatt see [7].Google Scholar
  2. 10.
    A.G.Hansen Similarity Analyses of Boundary Value Problems in Engineering Prentice-Hall, London, 1964.zbMATHGoogle Scholar

On differential geometry

  1. 11.
    A.R.Forsyth Lectures on the Differential Geometry of Curves and Surfaces Cambridge University Press, 1912.zbMATHGoogle Scholar
  2. 12.
    C.E.Weatherburn Differential Geometry of Three Dimensions Cambridge University Press, 1927, (*).zbMATHGoogle Scholar
  3. 13.
    D.J.Struik Lectures on Classical Differential Geometry Addison-Wesley, London, 1957, (*).Google Scholar

General Handbooks

  1. 14.
    A.M.Abramowitz I.A.Stegun Handbook of Mathematical Functions Dover, 1965.Google Scholar
  2. 15.
    I.S.Gradshteyn I.M.Ryzhik , Tables of Integrals Series and Products Academic Press, 1965.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1992

Authors and Affiliations

  • J. Molenaar
    • 1
  1. 1.Institute for Mathematics Consulting Faculty of Mathematics and Computing ScienceEindhoven University of TechnologyEindhovenThe Netherlands

Personalised recommendations