Fractional Analysis: Methods of Motion Decomposition - Hardcover

Novozhilov, I.V.

Hardcover

ISBN 10: 081763889X ISBN 13: 9780817638894

Publisher: Birkhäuser, 1997

Synopsis

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.

About this title

Synopsis

Developed and implemented by the author, this text describes a method of constructing approximate math models of finite-dimensional dynamic systems. Fractional analysis is used as a mathematical tool of the proposed method. Fractional analysis unites algorithms of similitude and dimensionality theory and algorithms of asympototic expansions in small parameter. The goal of the text is to apply the ideas of fractional analysis to finite-dimensional controlled systems.

From the Back Cover

The book deals with a method of formalized construction of approximate mathematical models of dynamic systems, which combines methods of similitude and perturbation theory and algorithms of asymptotic expansions in small parameter. This method was termed by Kline 'fractional analysis'.

Edition details

• Publisher: Birkhäuser
• Publication date: 1997
• ISBN 10: 081763889X
• ISBN 13: 9780817638894
• Binding: Hardcover
• Language: English
• Number of pages: 242