Fractional Analysis

Methods of Motion Decomposition

Authors: Novozhilov, I.V.

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About this book

This book considers methods of approximate analysis of mechanical, elec­ tromechanical, and other systems described by ordinary differential equa­ tions. Modern mathematical modeling of sophisticated mechanical systems consists of several stages: first, construction of a mechanical model, and then writing appropriate equations and their analytical or numerical ex­ amination. Usually, this procedure is repeated several times. Even if an initial model correctly reflects the main properties of a phenomenon, it de­ scribes, as a rule, many unnecessary details that make equations of motion too complicated. As experience and experimental data are accumulated, the researcher considers simpler models and simplifies the equations. Thus some terms are discarded, the order of the equations is lowered, and so on. This process requires time, experimentation, and the researcher's intu­ ition. A good example of such a semi-experimental way of simplifying is a gyroscopic precession equation. Formal mathematical proofs of its admis­ sibility appeared some several decades after its successful introduction in engineering calculations. Applied mathematics now has at its disposal many methods of approxi­ mate analysis of differential equations. Application of these methods could shorten and formalize the procedure of simplifying the equations and, thus, of constructing approximate motion models. Wide application of the methods into practice is hindered by the fol­ lowing. 1. Descriptions of various approximate methods are scattered over the mathematical literature. The researcher, as a rule, does not know what method is most suitable for a specific case. 2.

Table of contents (6 chapters)

  • Dimensional analysis and small parameters

    Novozhilov, Igor V.

    Pages 1-24

  • Regularly perturbed systems. Expansions of solutions

    Novozhilov, Igor V.

    Pages 25-41

  • Decomposition of motion in systems with fast phase

    Novozhilov, Igor V.

    Pages 43-86

  • Decomposition of motion in systems with boundary layer

    Novozhilov, Igor V.

    Pages 87-121

  • Decomposition of motion in systems with discontinuous characteristics

    Novozhilov, Igor V.

    Pages 123-135

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-1-4612-4130-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-0-8176-3889-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4612-8667-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fractional Analysis
Book Subtitle
Methods of Motion Decomposition
Authors
Copyright
1997
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-1-4612-4130-0
DOI
10.1007/978-1-4612-4130-0
Hardcover ISBN
978-0-8176-3889-4
Softcover ISBN
978-1-4612-8667-7
Edition Number
1
Number of Pages
X, 232
Topics