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Fractional Analysis - Methods of Motion Decomposition (Hardcover, 1997 ed.)
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Fractional Analysis - Methods of Motion Decomposition (Hardcover, 1997 ed.)
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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."
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