Poincare-Dulac method with Chebyshev economization in autonomous mechanical systems simulation problem

Author

Melnikov, V.G. ; Melnikov, G.I. ; Malykh, K.S. ; Dudarenko, N.A.

Author_Institution

ITMO Univ., St. Petersburg, Russia

fYear

2015

fDate

2-6 Feb. 2015

Firstpage

1

Lastpage

3

Abstract

We consider an equation of an autonomous dynamical system with one degree of freedom. It contains the linear and cubic forms relative to phase variables. In order to simplify the mathematical model we use the modified asymptotic method of Poincare-Dulac conversion. Using Chebyshev approximations of high-degree polynomials with polynomials of smaller degrees we reduce the residual error. We consider non-oscillatory mechanical systems in the case of absence of internal Poincare resonances that leads to a linear form.

Keywords

Chebyshev approximation; Poincare mapping; nonlinear dynamical systems; Chebyshev approximations; Chebyshev economization; Poincare-Dulac method; autonomous dynamical system; autonomous mechanical systems simulation; degree of freedom; high-degree polynomials; mathematical model; modified asymptotic method; nonoscillatory mechanical systems; phase variables; residual error; Accuracy; Chebyshev approximation; Friction; Mathematical model; Mechanical systems; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

Mechanics - Seventh Polyakhov's Reading, 2015 International Conference on

Conference_Location

Saint Petersburg

Type

conf

DOI

10.1109/POLYAKHOV.2015.7106757

Filename

7106757