Tricomi's Φ-equation
We study an autonomous nonlinear differential equation that models the movement of a damped F-pendulum with constant forcing. In the dissipative case, two results are presented, on the one hand, using the application of Poincaré and energy functions, a sufficient criterion is established to guarante...
- Autores:
-
Castro G., Diego A.
Gutiérrez G., Alexander
- Tipo de recurso:
- Fecha de publicación:
- 2018
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- spa
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/13189
- Acceso en línea:
- http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903
http://hdl.handle.net/10784/13189
- Palabra clave:
- Periodic solutions
Attractors
Stability
Soluciones periódicas
Atractores
Estabilidad
- Rights
- License
- Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G.
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2018-06-142018-11-16T16:28:59Z2018-06-142018-11-16T16:28:59Z2256-43141794-9165http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903http://hdl.handle.net/10784/1318910.17230/ingciencia.13.27.1We study an autonomous nonlinear differential equation that models the movement of a damped F-pendulum with constant forcing. In the dissipative case, two results are presented, on the one hand, using the application of Poincaré and energy functions, a sufficient criterion is established to guarantee the existence, uniqueness and asymptotic stability of a periodic solution of the second kind and on the other hand, a criterion is presented with which the basin of attraction of an asymptotically stable equilibrium is estimated analytically with the help of the Lasalle’s invariance principle. While in the conservative case there are necessary conditions for range of the period function to be defined in an unbounded interval. The results obtained in the dissipative case are a generalization of those established by Tricomi in the newtonian case.Se estudia una ecuación diferencial no lineal autónoma que modela el movimiento de un Φ-péndulo amortiguado con forzamiento constante. En el caso disipativo se presentan dos resultados, por un lado, usando la aplicación de Poincaré y funciones de energía, se establece un criterio suficiente para determinar la existencia, unicidad y estabilidad asintótica de una solución periódica de segunda clase y por otro lado, se presenta un criterio con el que se estima analíticamente la cuenca de atracción de un equilibrio asintóticamente estable con ayuda del principio de invarianza de Lasalle. Mientras que en el caso conservativo se dan condiciones necesarias para que la imagen de la función periodo esté definida en un intervalo no acotado. Los resultados obtenidos en el caso disipativo son una generalización de los establecidos por Tricomi en el caso newtoniano.application/pdfspaUniversidad EAFIThttp://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G.Attribution 4.0 International (CC BY 4.0)http://creativecommons.org/licenses/by/4.0Acceso abiertohttp://purl.org/coar/access_right/c_abf2instname:Universidad EAFITreponame:Repositorio Institucional Universidad EAFITIngeniería y Ciencia; Vol 14 No 27 (2018); 11-28Ingeniería y Ciencia; Vol 14 No 27 (2018); 11-28Tricomi's Φ-equationΦ-ecuación de Tricomiinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionarticlepublishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Periodic solutionsAttractorsStabilitySoluciones periódicasAtractoresEstabilidadCastro G., Diego A.Gutiérrez G., AlexanderUniversidad Tecnológica de PereiraIngeniería y Ciencia14271128ing.ciencTHUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/9cd67b8e-82b0-437d-8e3f-b06f785bdbb3/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINALdocument (4).pdfdocument (4).pdfTexto completo PDFapplication/pdf567257https://repository.eafit.edu.co/bitstreams/781b8bde-4c52-4364-a9b8-1ec039dbd1c7/download05ab42db00885e3d318e30e21f924f56MD52articulo.htmlarticulo.htmlTexto completo HTMLtext/html374https://repository.eafit.edu.co/bitstreams/66b34684-a58b-412e-822b-ea1396ede03a/downloadd3b00fce8feb26e4cc14cb0134f935b9MD5310784/13189oai:repository.eafit.edu.co:10784/131892020-03-01 12:44:55.607http://creativecommons.org/licenses/by/4.0Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G.open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
Tricomi's Φ-equation |
| dc.title.spa.fl_str_mv |
Φ-ecuación de Tricomi |
| title |
Tricomi's Φ-equation |
| spellingShingle |
Tricomi's Φ-equation Periodic solutions Attractors Stability Soluciones periódicas Atractores Estabilidad |
| title_short |
Tricomi's Φ-equation |
| title_full |
Tricomi's Φ-equation |
| title_fullStr |
Tricomi's Φ-equation |
| title_full_unstemmed |
Tricomi's Φ-equation |
| title_sort |
Tricomi's Φ-equation |
| dc.creator.fl_str_mv |
Castro G., Diego A. Gutiérrez G., Alexander |
| dc.contributor.author.none.fl_str_mv |
Castro G., Diego A. Gutiérrez G., Alexander |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad Tecnológica de Pereira |
| dc.subject.keyword.eng.fl_str_mv |
Periodic solutions Attractors Stability |
| topic |
Periodic solutions Attractors Stability Soluciones periódicas Atractores Estabilidad |
| dc.subject.keyword.spa.fl_str_mv |
Soluciones periódicas Atractores Estabilidad |
| description |
We study an autonomous nonlinear differential equation that models the movement of a damped F-pendulum with constant forcing. In the dissipative case, two results are presented, on the one hand, using the application of Poincaré and energy functions, a sufficient criterion is established to guarantee the existence, uniqueness and asymptotic stability of a periodic solution of the second kind and on the other hand, a criterion is presented with which the basin of attraction of an asymptotically stable equilibrium is estimated analytically with the help of the Lasalle’s invariance principle. While in the conservative case there are necessary conditions for range of the period function to be defined in an unbounded interval. The results obtained in the dissipative case are a generalization of those established by Tricomi in the newtonian case. |
| publishDate |
2018 |
| dc.date.available.none.fl_str_mv |
2018-11-16T16:28:59Z |
| dc.date.issued.none.fl_str_mv |
2018-06-14 |
| dc.date.accessioned.none.fl_str_mv |
2018-11-16T16:28:59Z |
| dc.date.none.fl_str_mv |
2018-06-14 |
| dc.type.eng.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion article publishedVersion |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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http://purl.org/coar/resource_type/c_6501 http://purl.org/coar/resource_type/c_2df8fbb1 |
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Artículo |
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publishedVersion |
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2256-4314 1794-9165 |
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http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903 http://hdl.handle.net/10784/13189 |
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10.17230/ingciencia.13.27.1 |
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2256-4314 1794-9165 10.17230/ingciencia.13.27.1 |
| url |
http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903 http://hdl.handle.net/10784/13189 |
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spa |
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spa |
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http://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/4903 |
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Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G. Attribution 4.0 International (CC BY 4.0) |
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http://creativecommons.org/licenses/by/4.0 |
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Acceso abierto |
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Copyright (c) 2018 Diego A. Castro G., Alexander Gutiérrez G. Attribution 4.0 International (CC BY 4.0) http://creativecommons.org/licenses/by/4.0 Acceso abierto http://purl.org/coar/access_right/c_abf2 |
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application/pdf |
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Universidad EAFIT |
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instname:Universidad EAFIT reponame:Repositorio Institucional Universidad EAFIT |
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Ingeniería y Ciencia; Vol 14 No 27 (2018); 11-28 |
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Ingeniería y Ciencia; Vol 14 No 27 (2018); 11-28 |
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