Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism

The slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (...

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Main Authors: Brahim Benhammouda, Hector Vazquez-Leal
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/206473
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author Brahim Benhammouda
Hector Vazquez-Leal
author_facet Brahim Benhammouda
Hector Vazquez-Leal
author_sort Brahim Benhammouda
collection DOAJ
description The slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (DAEs), and therefore difficult to integrate numerically. In this work, we present the application of the differential transform method (DTM) to obtain an approximate analytical solution of the SCM model in convergent series form. In addition, we propose a posttreatment of the power series solution with the Padé resummation method to extend the domain of convergence of the approximate series solution. The main advantage of the proposed technique is that it does not require an index reduction and does not generate secular terms or depend on a perturbation parameter.
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spelling doaj-art-4dcbce01395746c5b5335e5e724e877a2025-08-20T03:36:22ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/206473206473Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank MechanismBrahim Benhammouda0Hector Vazquez-Leal1Higher Colleges of Technology, Abu Dhabi Men’s College, P.O. Box 25035, Abu Dhabi, UAEElectronic Instrumentation and Atmospheric Sciences School, Universidad Veracruzana, Cto. Gonzalo Aguirre Beltrán S/N, 91000 Xalapa, VER, MexicoThe slider-crank mechanism (SCM) is one of the most important mechanisms in modern technology. It appears in most combustion engines including those of automobiles, trucks, and other small engines. The SCM model considered here is an index-three nonlinear system of differential-algebraic equations (DAEs), and therefore difficult to integrate numerically. In this work, we present the application of the differential transform method (DTM) to obtain an approximate analytical solution of the SCM model in convergent series form. In addition, we propose a posttreatment of the power series solution with the Padé resummation method to extend the domain of convergence of the approximate series solution. The main advantage of the proposed technique is that it does not require an index reduction and does not generate secular terms or depend on a perturbation parameter.http://dx.doi.org/10.1155/2015/206473
spellingShingle Brahim Benhammouda
Hector Vazquez-Leal
Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
Discrete Dynamics in Nature and Society
title Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
title_full Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
title_fullStr Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
title_full_unstemmed Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
title_short Analytical Solution of a Nonlinear Index-Three DAEs System Modelling a Slider-Crank Mechanism
title_sort analytical solution of a nonlinear index three daes system modelling a slider crank mechanism
url http://dx.doi.org/10.1155/2015/206473
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