A generalized Montgomery phase formula for rotating self-deforming bodies

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,...

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Detalles Bibliográficos
Autor principal: Cabrera, Alejandra Fabiana
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2007
Materias:
Matemática
Classical mechanics
Deformable bodies
Real and complex differential geometry
Reconstruction phases
Time dependent non-integrable classical systems
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/82971
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-82971
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Classical mechanics
Deformable bodies
Real and complex differential geometry
Reconstruction phases
Time dependent non-integrable classical systems
spellingShingle Matemática
Classical mechanics
Deformable bodies
Real and complex differential geometry
Reconstruction phases
Time dependent non-integrable classical systems
Cabrera, Alejandra Fabiana
A generalized Montgomery phase formula for rotating self-deforming bodies
topic_facet Matemática
Classical mechanics
Deformable bodies
Real and complex differential geometry
Reconstruction phases
Time dependent non-integrable classical systems
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 Δ T, 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.
format Articulo
Preprint
author Cabrera, Alejandra Fabiana
author_facet Cabrera, Alejandra Fabiana
author_sort Cabrera, Alejandra Fabiana
title A generalized Montgomery phase formula for rotating self-deforming bodies
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 generalized montgomery phase formula for rotating self-deforming bodies
publishDate 2007
url http://sedici.unlp.edu.ar/handle/10915/82971
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bdutipo_str Repositorios
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