TRANSFORMATION OF DYNAMIC POLYNOMIAL SYSTEMS BY CHEBYSHEV APPROXIMATION

Melnikov Vitaly G

2012 , VOLUME 12, NUMBER 4 ( July-August )

ISSN 2226-1494 (print), ISSN 2500-0373 (online)

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Nikiforov
Vladimir O.
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TRANSFORMATION OF DYNAMIC POLYNOMIAL SYSTEMS BY CHEBYSHEV APPROXIMATION

V. G. Melnikov

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Abstract

This paper presents a new method of nonlinear model simplification for mechanical control systems presented by an autonomous differential equations system of a polynomial structure connected with Poincare-Dulac normalization method. Change in the method is made consisting in approximation of high degrees remainder terms by less degree polynomials with their saving in the equations and significant rise of changed system accuracy. The problem of transformation of phase variables for simplification of a mathematical model is
considered. Chebyshev economization method is used to approximate remainder terms.

Keywords: autonomous system of dynamic equations, polynomial transformation of phase coordinates, Poincare-Dulac normal forms, Chebyshev approximations

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