Some nonlinear mechanical problems solved with analytical solutions

Autores
Filipich, Carlos Pedro; Rosales, Marta Beatriz; Buezas, Fernando Salvador
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper the analytical solution of nonlinear ordinary differential systems is addressed. Some of the problems are classical in the related literature and exhibit chaotic behavior in certain ranges of the involved parameters despite being simple-looking deterministic systems. The solutions are approached by means of the old technique of power series to solve ordinary differential equations. The independent variable is time in all the illustrations and elementary recurrence algorithms are obtained. This is an alternative to the standard numerical techniques and ensures the theoretical exactness of the response. Several examples are included and trajectories diagrams, phase plots, etc. are shown. The desired numerical precision is attained using time steps several times larger than the usual ones. The availability of an analytical solution may be an additional tool within a standard qualitative analysis. The solution of higher order problems and governed by partial differential equations is under study.
Fil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional; Argentina
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería. Área Estabilidad; Argentina
Fil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina
Materia
NONLINEAR SYSTEM EQUATIONS
POWER SERIES
MECHANICAL PROBLEMS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/98568
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Some nonlinear mechanical problems solved with analytical solutionsFilipich, Carlos PedroRosales, Marta BeatrizBuezas, Fernando SalvadorNONLINEAR SYSTEM EQUATIONSPOWER SERIESMECHANICAL PROBLEMShttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2In this paper the analytical solution of nonlinear ordinary differential systems is addressed. Some of the problems are classical in the related literature and exhibit chaotic behavior in certain ranges of the involved parameters despite being simple-looking deterministic systems. The solutions are approached by means of the old technique of power series to solve ordinary differential equations. The independent variable is time in all the illustrations and elementary recurrence algorithms are obtained. This is an alternative to the standard numerical techniques and ensures the theoretical exactness of the response. Several examples are included and trajectories diagrams, phase plots, etc. are shown. The desired numerical precision is attained using time steps several times larger than the usual ones. The availability of an analytical solution may be an additional tool within a standard qualitative analysis. The solution of higher order problems and governed by partial differential equations is under study.Fil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional; ArgentinaFil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería. Área Estabilidad; ArgentinaFil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Física; ArgentinaPlanta Piloto de Ingeniería Química2004-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/98568Filipich, Carlos Pedro; Rosales, Marta Beatriz; Buezas, Fernando Salvador; Some nonlinear mechanical problems solved with analytical solutions; Planta Piloto de Ingeniería Química; Latin American Applied Research; 34; 2; 4-2004; 101-1090327-07931851-8796CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327-07932004000200005&lng=es&nrm=isoinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:06:37Zoai:ri.conicet.gov.ar:11336/98568instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:06:37.998CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some nonlinear mechanical problems solved with analytical solutions
title Some nonlinear mechanical problems solved with analytical solutions
spellingShingle Some nonlinear mechanical problems solved with analytical solutions
Filipich, Carlos Pedro
NONLINEAR SYSTEM EQUATIONS
POWER SERIES
MECHANICAL PROBLEMS
title_short Some nonlinear mechanical problems solved with analytical solutions
title_full Some nonlinear mechanical problems solved with analytical solutions
title_fullStr Some nonlinear mechanical problems solved with analytical solutions
title_full_unstemmed Some nonlinear mechanical problems solved with analytical solutions
title_sort Some nonlinear mechanical problems solved with analytical solutions
dc.creator.none.fl_str_mv Filipich, Carlos Pedro
Rosales, Marta Beatriz
Buezas, Fernando Salvador
author Filipich, Carlos Pedro
author_facet Filipich, Carlos Pedro
Rosales, Marta Beatriz
Buezas, Fernando Salvador
author_role author
author2 Rosales, Marta Beatriz
Buezas, Fernando Salvador
author2_role author
author
dc.subject.none.fl_str_mv NONLINEAR SYSTEM EQUATIONS
POWER SERIES
MECHANICAL PROBLEMS
topic NONLINEAR SYSTEM EQUATIONS
POWER SERIES
MECHANICAL PROBLEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv In this paper the analytical solution of nonlinear ordinary differential systems is addressed. Some of the problems are classical in the related literature and exhibit chaotic behavior in certain ranges of the involved parameters despite being simple-looking deterministic systems. The solutions are approached by means of the old technique of power series to solve ordinary differential equations. The independent variable is time in all the illustrations and elementary recurrence algorithms are obtained. This is an alternative to the standard numerical techniques and ensures the theoretical exactness of the response. Several examples are included and trajectories diagrams, phase plots, etc. are shown. The desired numerical precision is attained using time steps several times larger than the usual ones. The availability of an analytical solution may be an additional tool within a standard qualitative analysis. The solution of higher order problems and governed by partial differential equations is under study.
Fil: Filipich, Carlos Pedro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Universidad Tecnológica Nacional; Argentina
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería. Área Estabilidad; Argentina
Fil: Buezas, Fernando Salvador. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Unidad de Direccion; Argentina. Universidad Nacional del Sur. Departamento de Física; Argentina
description In this paper the analytical solution of nonlinear ordinary differential systems is addressed. Some of the problems are classical in the related literature and exhibit chaotic behavior in certain ranges of the involved parameters despite being simple-looking deterministic systems. The solutions are approached by means of the old technique of power series to solve ordinary differential equations. The independent variable is time in all the illustrations and elementary recurrence algorithms are obtained. This is an alternative to the standard numerical techniques and ensures the theoretical exactness of the response. Several examples are included and trajectories diagrams, phase plots, etc. are shown. The desired numerical precision is attained using time steps several times larger than the usual ones. The availability of an analytical solution may be an additional tool within a standard qualitative analysis. The solution of higher order problems and governed by partial differential equations is under study.
publishDate 2004
dc.date.none.fl_str_mv 2004-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/98568
Filipich, Carlos Pedro; Rosales, Marta Beatriz; Buezas, Fernando Salvador; Some nonlinear mechanical problems solved with analytical solutions; Planta Piloto de Ingeniería Química; Latin American Applied Research; 34; 2; 4-2004; 101-109
0327-0793
1851-8796
CONICET Digital
CONICET
url http://hdl.handle.net/11336/98568
identifier_str_mv Filipich, Carlos Pedro; Rosales, Marta Beatriz; Buezas, Fernando Salvador; Some nonlinear mechanical problems solved with analytical solutions; Planta Piloto de Ingeniería Química; Latin American Applied Research; 34; 2; 4-2004; 101-109
0327-0793
1851-8796
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.scielo.org.ar/scielo.php?script=sci_arttext&pid=S0327-07932004000200005&lng=es&nrm=iso
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
publisher.none.fl_str_mv Planta Piloto de Ingeniería Química
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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