Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints

In this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system,...

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Detalhes bibliográficos
Autores: García-Agúndez Blanco, Alfonso, García Vallejo, Daniel, Freire Macías, Emilio
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2024
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/155680
Acesso em linha:https://hdl.handle.net/11441/155680
https://doi.org/10.1007/s11071-023-09178-z
Access Level:Acceso aberto
Palavra-chave:Toroidal wheel
Nonholonomic systems
Linearization
Stability analysis
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spelling Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraintsGarcía-Agúndez Blanco, AlfonsoGarcía Vallejo, DanielFreire Macías, EmilioToroidal wheelNonholonomic systemsLinearizationStability analysisIn this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system, given by the dynamic equilibrium equations augmented with the nonholonomic constraints, which arise from the no-slip condition. The circular steady motion and the linearized equations of motion along this relative equilibrium are obtained, for both the solid and hollow tori. The expressions of the linearized equations and the corresponding eigenvalues are derived analytically as a function of the torus aspect ratio. The variation of the stability boundary with the torus aspect ratio is shown. A comparison of the results obtained in the solid and hollow scenarios is included, and all the results are validated with the rolling hoop, which corresponds to a degenerate torus with zero aspect ratio. In the particular case of the steady straight-line rolling and spinning about a vertical diameter, which constitute limit motions of the circular steady motion, the critical rotational and angular speeds required for stabilization are obtained.SpringerIngeniería Mecánica y FabricaciónMatemática Aplicada IITEP111: Ingeniería MecánicaTIC130: Investigación en Sistemas Dinámicos en IngenieríaMinisterio de Ciencia, Innovación y Universidades (MICINN). EspañaJunta de Andalucía2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/155680https://doi.org/10.1007/s11071-023-09178-zreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Dynamics, 112 (4), 2453-2476.FPU18/05598US-1380740https://link.springer.com/article/10.1007/s11071-023-09178-zinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1556802026-06-17T12:51:07Z
dc.title.none.fl_str_mv Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
title Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
spellingShingle Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
García-Agúndez Blanco, Alfonso
Toroidal wheel
Nonholonomic systems
Linearization
Stability analysis
title_short Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
title_full Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
title_fullStr Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
title_full_unstemmed Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
title_sort Analytical and numerical stability analysis of a toroidal wheel with nonholonomic constraints
dc.creator.none.fl_str_mv García-Agúndez Blanco, Alfonso
García Vallejo, Daniel
Freire Macías, Emilio
author García-Agúndez Blanco, Alfonso
author_facet García-Agúndez Blanco, Alfonso
García Vallejo, Daniel
Freire Macías, Emilio
author_role author
author2 García Vallejo, Daniel
Freire Macías, Emilio
author2_role author
author
dc.contributor.none.fl_str_mv Ingeniería Mecánica y Fabricación
Matemática Aplicada II
TEP111: Ingeniería Mecánica
TIC130: Investigación en Sistemas Dinámicos en Ingeniería
Ministerio de Ciencia, Innovación y Universidades (MICINN). España
Junta de Andalucía
dc.subject.none.fl_str_mv Toroidal wheel
Nonholonomic systems
Linearization
Stability analysis
topic Toroidal wheel
Nonholonomic systems
Linearization
Stability analysis
description In this paper, a detailed and comprehensive linear stability analysis of a rolling toroidal wheel is performed. The wheel is modeled as a rigid toroid-shaped body rolling without slipping on a horizontal surface. The nonlinear equations of motion constitute a Differential-Algebraic Equations system, given by the dynamic equilibrium equations augmented with the nonholonomic constraints, which arise from the no-slip condition. The circular steady motion and the linearized equations of motion along this relative equilibrium are obtained, for both the solid and hollow tori. The expressions of the linearized equations and the corresponding eigenvalues are derived analytically as a function of the torus aspect ratio. The variation of the stability boundary with the torus aspect ratio is shown. A comparison of the results obtained in the solid and hollow scenarios is included, and all the results are validated with the rolling hoop, which corresponds to a degenerate torus with zero aspect ratio. In the particular case of the steady straight-line rolling and spinning about a vertical diameter, which constitute limit motions of the circular steady motion, the critical rotational and angular speeds required for stabilization are obtained.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/155680
https://doi.org/10.1007/s11071-023-09178-z
url https://hdl.handle.net/11441/155680
https://doi.org/10.1007/s11071-023-09178-z
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Dynamics, 112 (4), 2453-2476.
FPU18/05598
US-1380740
https://link.springer.com/article/10.1007/s11071-023-09178-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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