Numerical stabilization of the Levitron's realistic model

The stability of the magnetic levitation showed by the Levit- 10 ron was studied by M.V. Berry as a six degrees of freedom Hamiltonian 11 system using an adiabatic approximation. Further, H.R. Dullin found 12 critical spin rate bounds where the levitation persist and R.F. Gans 13 et al. offered nume...

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Autores principales: Olverá, Arturo, De la Rosa, Abraham, Giordano, Claudia Marcela
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2016
Materias:
Ciencias Astronómicas
Levitron
Dynamics (galaxias)
Chaos
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/93934
https://link.springer.com/article/10.1140%2Fepjst%2Fe2016-60005-3
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-93934
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Ciencias Astronómicas
Levitron
Dynamics (galaxias)
Chaos
spellingShingle Ciencias Astronómicas
Levitron
Dynamics (galaxias)
Chaos
Olverá, Arturo
De la Rosa, Abraham
Giordano, Claudia Marcela
Numerical stabilization of the Levitron's realistic model
topic_facet Ciencias Astronómicas
Levitron
Dynamics (galaxias)
Chaos
description The stability of the magnetic levitation showed by the Levit- 10 ron was studied by M.V. Berry as a six degrees of freedom Hamiltonian 11 system using an adiabatic approximation. Further, H.R. Dullin found 12 critical spin rate bounds where the levitation persist and R.F. Gans 13 et al. offered numerical results regarding the initial conditions’ manifold 14 where this occurs. In the line of this series of works, first, we extend the 15 equations of motion to include dissipation for a more realistic model, 16 and then introduce a mechanical forcing to inject energy into the sys- 17 tem in order to prevent the Levitron from falling. A systematic study 18 of the flying time as a function of the forcing parameters is carried out 19 which yields detailed bifurcation diagrams showing an Arnold’s tongues 20 structure. The stability of these solutions were studied with the help 21 of a novel method to compute the maximum Lyapunov exponent called 22 MEGNO. The bifurcation diagrams for MEGNO reproduce the same 23 Arnold’s tongue structure.
format Articulo
Preprint
author Olverá, Arturo
De la Rosa, Abraham
Giordano, Claudia Marcela
author_facet Olverá, Arturo
De la Rosa, Abraham
Giordano, Claudia Marcela
author_sort Olverá, Arturo
title Numerical stabilization of the Levitron's realistic model
title_short Numerical stabilization of the Levitron's realistic model
title_full Numerical stabilization of the Levitron's realistic model
title_fullStr Numerical stabilization of the Levitron's realistic model
title_full_unstemmed Numerical stabilization of the Levitron's realistic model
title_sort numerical stabilization of the levitron's realistic model
publishDate 2016
url http://sedici.unlp.edu.ar/handle/10915/93934
https://link.springer.com/article/10.1140%2Fepjst%2Fe2016-60005-3
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AT delarosaabraham numericalstabilizationofthelevitronsrealisticmodel
AT giordanoclaudiamarcela numericalstabilizationofthelevitronsrealisticmodel
bdutipo_str Repositorios
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