A generalized Montgomery phase formula for rotating self-deforming bodies

Autores
Cabrera, Alejandro
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the motion of self-deforming bodies with non-zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time , this curve is simple and closed, the deforming body’s orientation in space is fully characterized by an angle or phase θM. We also give a reconstruction formula for this angle which generalizes R. Montgomery’s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.
Fil: Cabrera, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
Materia
DEFORMABLE BODIES
RECONSTRUCTION PHASES
TIME DEPENDENT NON-INTEGRABLE CLASSICAL SYSTEMS
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:11336/241811
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling A generalized Montgomery phase formula for rotating self-deforming bodiesCabrera, AlejandroDEFORMABLE BODIESRECONSTRUCTION PHASESTIME DEPENDENT NON-INTEGRABLE CLASSICAL SYSTEMShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the motion of self-deforming bodies with non-zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time , this curve is simple and closed, the deforming body’s orientation in space is fully characterized by an angle or phase θM. We also give a reconstruction formula for this angle which generalizes R. Montgomery’s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.Fil: Cabrera, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; ArgentinaElsevier Science2007-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/241811Cabrera, Alejandro; A generalized Montgomery phase formula for rotating self-deforming bodies; Elsevier Science; Journal Of Geometry And Physics; 57; 5; 4-2007; 1405-14200393-0440CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044006001616info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2006.11.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:39:09Zoai:ri.conicet.gov.ar:11336/241811instacron: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 10:39:09.717CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A generalized Montgomery phase formula for rotating self-deforming bodies
title A generalized Montgomery phase formula for rotating self-deforming bodies
spellingShingle A generalized Montgomery phase formula for rotating self-deforming bodies
Cabrera, Alejandro
DEFORMABLE BODIES
RECONSTRUCTION PHASES
TIME DEPENDENT NON-INTEGRABLE CLASSICAL SYSTEMS
title_short A generalized Montgomery phase formula for rotating self-deforming bodies
title_full A generalized Montgomery phase formula for rotating self-deforming bodies
title_fullStr A generalized Montgomery phase formula for rotating self-deforming bodies
title_full_unstemmed A generalized Montgomery phase formula for rotating self-deforming bodies
title_sort A generalized Montgomery phase formula for rotating self-deforming bodies
dc.creator.none.fl_str_mv Cabrera, Alejandro
author Cabrera, Alejandro
author_facet Cabrera, Alejandro
author_role author
dc.subject.none.fl_str_mv DEFORMABLE BODIES
RECONSTRUCTION PHASES
TIME DEPENDENT NON-INTEGRABLE CLASSICAL SYSTEMS
topic DEFORMABLE BODIES
RECONSTRUCTION PHASES
TIME DEPENDENT NON-INTEGRABLE CLASSICAL SYSTEMS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study the motion of self-deforming bodies with non-zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time , this curve is simple and closed, the deforming body’s orientation in space is fully characterized by an angle or phase θM. We also give a reconstruction formula for this angle which generalizes R. Montgomery’s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.
Fil: Cabrera, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina
description We study the motion of self-deforming bodies with non-zero angular momentum when the changing shape is known as a function of time. The conserved angular momentum with respect to the center of mass, when seen from a rotating frame, describes a curve on a sphere as happens for the rigid body motion, though obeying a more complicated non-autonomous equation. We observe that if, after time , this curve is simple and closed, the deforming body’s orientation in space is fully characterized by an angle or phase θM. We also give a reconstruction formula for this angle which generalizes R. Montgomery’s well known formula for the rigid body phase. Finally, we apply these techniques to obtain analytical results on the motion of deforming bodies in some concrete examples.
publishDate 2007
dc.date.none.fl_str_mv 2007-04
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/11336/241811
Cabrera, Alejandro; A generalized Montgomery phase formula for rotating self-deforming bodies; Elsevier Science; Journal Of Geometry And Physics; 57; 5; 4-2007; 1405-1420
0393-0440
CONICET Digital
CONICET
url http://hdl.handle.net/11336/241811
identifier_str_mv Cabrera, Alejandro; A generalized Montgomery phase formula for rotating self-deforming bodies; Elsevier Science; Journal Of Geometry And Physics; 57; 5; 4-2007; 1405-1420
0393-0440
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0393044006001616
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.geomphys.2006.11.003
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
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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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