Regular and chaotic phase space fraction in the double pendulum
Resumen:
The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the system passes through values where chaotic trajectories are abundant, and then, increasing the energy further, it is again dominated by regular trajectories. Given that the energetically accessible states are bounded, a relevant question is about the fraction of phase space regular or chaotic trajectories as the energy varies. In this paper, we calculate the relative abundance of chaotic trajectories in phase space, characterizing the trajectories using the maximum Lyapunov exponent, and find that, for low energies, it grows exponentially.
| 2023 | |
| Nonlinear Sciences - Chaotic Dynamics | |
| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/42342 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución (CC - By 4.0) |
| _version_ | 1807522805952020480 |
|---|---|
| author | Cabrera, Santiago |
| author2 | Leonel, Edson D. Martí, Arturo |
| author2_role | author author |
| author_facet | Cabrera, Santiago Leonel, Edson D. Martí, Arturo |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Cabrera Santiago, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física. Leonel Edson D. Martí Arturo, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física. |
| dc.creator.none.fl_str_mv | Cabrera, Santiago Leonel, Edson D. Martí, Arturo |
| dc.date.accessioned.none.fl_str_mv | 2024-02-01T19:05:56Z |
| dc.date.available.none.fl_str_mv | 2024-02-01T19:05:56Z |
| dc.date.issued.none.fl_str_mv | 2023 |
| dc.description.abstract.none.fl_txt_mv | The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the system passes through values where chaotic trajectories are abundant, and then, increasing the energy further, it is again dominated by regular trajectories. Given that the energetically accessible states are bounded, a relevant question is about the fraction of phase space regular or chaotic trajectories as the energy varies. In this paper, we calculate the relative abundance of chaotic trajectories in phase space, characterizing the trajectories using the maximum Lyapunov exponent, and find that, for low energies, it grows exponentially. |
| dc.format.extent.es.fl_str_mv | 10 h. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Cabrera, S, Leonel, E y Martí, A. "Regular and chaotic phase space fraction in the double pendulum" [Preprint]. Publicado en: Chaotic Dynamics. 2023, arXiv:2312.13436, dec 2023. 10 h. DOI: 10.48550/arXiv.2312.13436 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2312.13436 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/42342 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.relation.ispartof.es.fl_str_mv | Chaotic Dynamics, arXiv:2312.13436, dec 2023. |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.es.fl_str_mv | Nonlinear Sciences - Chaotic Dynamics |
| dc.title.none.fl_str_mv | Regular and chaotic phase space fraction in the double pendulum |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the system passes through values where chaotic trajectories are abundant, and then, increasing the energy further, it is again dominated by regular trajectories. Given that the energetically accessible states are bounded, a relevant question is about the fraction of phase space regular or chaotic trajectories as the energy varies. In this paper, we calculate the relative abundance of chaotic trajectories in phase space, characterizing the trajectories using the maximum Lyapunov exponent, and find that, for low energies, it grows exponentially. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_2a97730e817d67358a0d95b5c697ea41 |
| identifier_str_mv | Cabrera, S, Leonel, E y Martí, A. "Regular and chaotic phase space fraction in the double pendulum" [Preprint]. Publicado en: Chaotic Dynamics. 2023, arXiv:2312.13436, dec 2023. 10 h. DOI: 10.48550/arXiv.2312.13436 10.48550/arXiv.2312.13436 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/42342 |
| publishDate | 2023 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución (CC - By 4.0) |
| spelling | Cabrera Santiago, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.Leonel Edson D.Martí Arturo, Universidad de la República (Uruguay). Facultad de Ciencias. Instituto de Física.2024-02-01T19:05:56Z2024-02-01T19:05:56Z2023Cabrera, S, Leonel, E y Martí, A. "Regular and chaotic phase space fraction in the double pendulum" [Preprint]. Publicado en: Chaotic Dynamics. 2023, arXiv:2312.13436, dec 2023. 10 h. DOI: 10.48550/arXiv.2312.13436https://hdl.handle.net/20.500.12008/4234210.48550/arXiv.2312.13436The double coplanar pendulum is an example of the coexistence of regular and chaotic dynamics for equal energy values but different initial conditions. Regular trajectories predominate for low energies; as the energy is increased, the system passes through values where chaotic trajectories are abundant, and then, increasing the energy further, it is again dominated by regular trajectories. Given that the energetically accessible states are bounded, a relevant question is about the fraction of phase space regular or chaotic trajectories as the energy varies. In this paper, we calculate the relative abundance of chaotic trajectories in phase space, characterizing the trajectories using the maximum Lyapunov exponent, and find that, for low energies, it grows exponentially.Submitted by Pintos Natalia (nataliapintosmvd@gmail.com) on 2024-01-31T17:14:30Z No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2312.13436.pdf: 12650772 bytes, checksum: af0752999473695ee6a4eebe01df3a85 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-02-01T12:20:41Z (GMT) No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2312.13436.pdf: 12650772 bytes, checksum: af0752999473695ee6a4eebe01df3a85 (MD5)Made available in DSpace by Seroubian Mabel (mabel.seroubian@seciu.edu.uy) on 2024-02-01T19:05:56Z (GMT). No. of bitstreams: 2 license_rdf: 24251 bytes, checksum: 71ed42ef0a0b648670f707320be37b90 (MD5) 10.48550.arXiv.2312.13436.pdf: 12650772 bytes, checksum: af0752999473695ee6a4eebe01df3a85 (MD5) Previous issue date: 202310 h.application/pdfenengChaotic Dynamics, arXiv:2312.13436, dec 2023.Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución (CC - By 4.0)Nonlinear Sciences - Chaotic DynamicsRegular and chaotic phase space fraction in the double pendulumPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaCabrera, SantiagoLeonel, Edson D.Martí, ArturoLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/42342/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-844http://localhost:8080/xmlui/bitstream/20.500.12008/42342/2/license_urla0ebbeafb9d2ec7cbb19d7137ebc392cMD52license_textlicense_texttext/html; charset=utf-820555http://localhost:8080/xmlui/bitstream/20.500.12008/42342/3/license_textc3353adb4b970603e3b1fce8a9e67d6cMD53license_rdflicense_rdfapplication/rdf+xml; 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- Universidad de la Repúblicafalse |
| spellingShingle | Regular and chaotic phase space fraction in the double pendulum Cabrera, Santiago Nonlinear Sciences - Chaotic Dynamics |
| status_str | submittedVersion |
| title | Regular and chaotic phase space fraction in the double pendulum |
| title_full | Regular and chaotic phase space fraction in the double pendulum |
| title_fullStr | Regular and chaotic phase space fraction in the double pendulum |
| title_full_unstemmed | Regular and chaotic phase space fraction in the double pendulum |
| title_short | Regular and chaotic phase space fraction in the double pendulum |
| title_sort | Regular and chaotic phase space fraction in the double pendulum |
| topic | Nonlinear Sciences - Chaotic Dynamics |
| url | https://hdl.handle.net/20.500.12008/42342 |
