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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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/206473 |
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| _version_ | 1849406509399670784 |
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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. |
| format | Article |
| id | doaj-art-4dcbce01395746c5b5335e5e724e877a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| 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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