Global study of the simple pendulum by the homotopy analysis method

Autores
Bel, Andrea Liliana; Reartes, Walter; Torresi, Ana María Luján
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Techniques are developed to find all periodic solutions in the simple pendulum by means of the homotopy analysis method (HAM). This involves the solution of the equations of motion in two different coordinate representations. Expressions are obtained for the cycles and periods of oscillations with a high degree of accuracy in the whole range of amplitudes. Moreover, the convergence of the method is easily checked. The aim of this work is to show how the dynamics of a simple example of oscillatory systems may be studied globally with the HAM and to incentivize the interest of advanced undergraduate students in this type of techniques.
Fil: Bel, Andrea Liliana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Reartes, Walter. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Materia
pendulum
homotopy analysis method
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:11336/188928
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Global study of the simple pendulum by the homotopy analysis methodBel, Andrea LilianaReartes, WalterTorresi, Ana María Lujánpendulumhomotopy analysis methodhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Techniques are developed to find all periodic solutions in the simple pendulum by means of the homotopy analysis method (HAM). This involves the solution of the equations of motion in two different coordinate representations. Expressions are obtained for the cycles and periods of oscillations with a high degree of accuracy in the whole range of amplitudes. Moreover, the convergence of the method is easily checked. The aim of this work is to show how the dynamics of a simple example of oscillatory systems may be studied globally with the HAM and to incentivize the interest of advanced undergraduate students in this type of techniques.Fil: Bel, Andrea Liliana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; ArgentinaFil: Reartes, Walter. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaFil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; ArgentinaIOP Publishing2012-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/188928Bel, Andrea Liliana; Reartes, Walter; Torresi, Ana María Luján; Global study of the simple pendulum by the homotopy analysis method; IOP Publishing; European Journal of Physics; 33; 2; 1-2012; 231-2410143-0807CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/33/2/231info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0143-0807/33/2/231info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:58Zoai:ri.conicet.gov.ar:11336/188928instacron: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:34982025-09-29 10:12:59.063CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global study of the simple pendulum by the homotopy analysis method
title Global study of the simple pendulum by the homotopy analysis method
spellingShingle Global study of the simple pendulum by the homotopy analysis method
Bel, Andrea Liliana
pendulum
homotopy analysis method
title_short Global study of the simple pendulum by the homotopy analysis method
title_full Global study of the simple pendulum by the homotopy analysis method
title_fullStr Global study of the simple pendulum by the homotopy analysis method
title_full_unstemmed Global study of the simple pendulum by the homotopy analysis method
title_sort Global study of the simple pendulum by the homotopy analysis method
dc.creator.none.fl_str_mv Bel, Andrea Liliana
Reartes, Walter
Torresi, Ana María Luján
author Bel, Andrea Liliana
author_facet Bel, Andrea Liliana
Reartes, Walter
Torresi, Ana María Luján
author_role author
author2 Reartes, Walter
Torresi, Ana María Luján
author2_role author
author
dc.subject.none.fl_str_mv pendulum
homotopy analysis method
topic pendulum
homotopy analysis method
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Techniques are developed to find all periodic solutions in the simple pendulum by means of the homotopy analysis method (HAM). This involves the solution of the equations of motion in two different coordinate representations. Expressions are obtained for the cycles and periods of oscillations with a high degree of accuracy in the whole range of amplitudes. Moreover, the convergence of the method is easily checked. The aim of this work is to show how the dynamics of a simple example of oscillatory systems may be studied globally with the HAM and to incentivize the interest of advanced undergraduate students in this type of techniques.
Fil: Bel, Andrea Liliana. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina
Fil: Reartes, Walter. Universidad Nacional del Sur. Departamento de Matemática; Argentina
Fil: Torresi, Ana María Luján. Universidad Nacional del Sur. Departamento de Matemática; Argentina
description Techniques are developed to find all periodic solutions in the simple pendulum by means of the homotopy analysis method (HAM). This involves the solution of the equations of motion in two different coordinate representations. Expressions are obtained for the cycles and periods of oscillations with a high degree of accuracy in the whole range of amplitudes. Moreover, the convergence of the method is easily checked. The aim of this work is to show how the dynamics of a simple example of oscillatory systems may be studied globally with the HAM and to incentivize the interest of advanced undergraduate students in this type of techniques.
publishDate 2012
dc.date.none.fl_str_mv 2012-01
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/11336/188928
Bel, Andrea Liliana; Reartes, Walter; Torresi, Ana María Luján; Global study of the simple pendulum by the homotopy analysis method; IOP Publishing; European Journal of Physics; 33; 2; 1-2012; 231-241
0143-0807
CONICET Digital
CONICET
url http://hdl.handle.net/11336/188928
identifier_str_mv Bel, Andrea Liliana; Reartes, Walter; Torresi, Ana María Luján; Global study of the simple pendulum by the homotopy analysis method; IOP Publishing; European Journal of Physics; 33; 2; 1-2012; 231-241
0143-0807
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/0143-0807/33/2/231
info:eu-repo/semantics/altIdentifier/url/https://iopscience.iop.org/article/10.1088/0143-0807/33/2/231
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
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 13.070432

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