Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables
In this work we study the attitude dynamics of a deformable gyrostat (or dual-spin spacecraft) in absence of external forces. Here, deformable means that one of the moments of inertia is a periodic function of time. This model is a more realistic approximation to the motion of a gyrostat than the pe...
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Universidad de Zaragoza (España)
1998
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oai-TES00000000242017-10-19Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variablesIñarrea Las Heras, ManuelIn this work we study the attitude dynamics of a deformable gyrostat (or dual-spin spacecraft) in absence of external forces. Here, deformable means that one of the moments of inertia is a periodic function of time. This model is a more realistic approximation to the motion of a gyrostat than the perfectly rigid model, and reveals chaotic phenomena in the dynamics of the system. In Chapter 1, we develop the Hamiltonian formulation corresponding to a generic free gyrostat with 3 rotors aligned with any different directions. We treat the problem in noncanonical variables: the components of the total angular momentum in the body frame. Then we focus on the particular case of a free triaxial deformable gyrostat whose Hamiltonian is a sum of an integrable part plus a timeperiodic perturbation. In Chapter 2, we consider the gyrostat when the rotors are at relative rest. By means of the Melnikov's method, we show that the gyrostat exhibits chaotic motion. The Melnikov function gives us an analytical estimation of the width of the stochastic layer generated by the perturbation. We check the validity of this analytical estimation calculating another numerical estimation. We find some deviations between both estimations due to the effect of nonlinear resonances. Chapters 3 and 4 focus on the gyrostat with one rotor in relative motion with respect to the platform. This spinning rotor is parallel to one of the principal axes of the gyrostat. By means of the Melnikov method and Poincaré surfaces of section we prove that the system also exhibits chaotic motion and that it can be removed if the spinning rotor reaches a relative angular momentum high enough. In Chapter 5 we study the reorientation process of the gyrostat and the effect of the perturbation in it. In order to show the influence of the perturbation, a suitable numerical parameter is introduced and it is related with the Melnikov function calculated in Chapter 2. Also we take into account the effect of nonlinear resonances to explain the sudden increments of the chaotic degree of the system.Universidad de Zaragoza (España)Lanchares Barrasa, Víctor (Universidad de La Rioja)1998text (thesis)application/pdfhttps://dialnet.unirioja.es/servlet/oaites?codigo=141(Tesis) ISBN 84-688-1525-X spaLICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI | INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI |
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In this work we study the attitude dynamics of a deformable gyrostat (or dual-spin spacecraft) in absence of external forces. Here, deformable means that one of the moments of inertia is a periodic function of time. This model is a more realistic approximation to the motion of a gyrostat than the perfectly rigid model, and reveals chaotic phenomena in the dynamics of the system.
In Chapter 1, we develop the Hamiltonian formulation corresponding to a generic free gyrostat with 3 rotors aligned with any different directions. We treat the problem in noncanonical variables: the components of the total angular momentum in the body frame. Then we focus on the particular case of a free triaxial deformable gyrostat whose Hamiltonian is a sum of an integrable part plus a timeperiodic perturbation.
In Chapter 2, we consider the gyrostat when the rotors are at relative rest. By means of the Melnikov's method, we show that the gyrostat exhibits chaotic motion. The Melnikov function gives us an analytical estimation of the width of the stochastic layer generated by the perturbation. We check the validity of this analytical estimation calculating another numerical estimation. We find some deviations between both estimations due to the effect of nonlinear resonances.
Chapters 3 and 4 focus on the gyrostat with one rotor in relative motion with respect to the platform. This spinning rotor is parallel to one of the principal axes of the gyrostat. By means of the Melnikov method and Poincaré surfaces of section we prove that the system also exhibits chaotic motion and that it can be removed if the spinning rotor reaches a relative angular momentum high enough.
In Chapter 5 we study the reorientation process of the gyrostat and the effect of the perturbation in it. In order to show the influence of the perturbation, a suitable numerical parameter is introduced and it is related with the Melnikov function calculated in Chapter 2. Also we take into account the effect of nonlinear resonances to explain the sudden increments of the chaotic degree of the system. |
| author2 |
Lanchares Barrasa, Víctor (Universidad de La Rioja) |
| author_facet |
Lanchares Barrasa, Víctor (Universidad de La Rioja) Iñarrea Las Heras, Manuel |
| format |
text (thesis) |
| author |
Iñarrea Las Heras, Manuel |
| spellingShingle |
Iñarrea Las Heras, Manuel Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| author_sort |
Iñarrea Las Heras, Manuel |
| title |
Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| title_short |
Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| title_full |
Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| title_fullStr |
Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| title_full_unstemmed |
Método de Melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| title_sort |
método de melnikov, bandas de estocasticidad y no integrabilidad en un giróstato con momentos de inercia variables |
| publisher |
Universidad de Zaragoza (España) |
| publishDate |
1998 |
| url |
https://dialnet.unirioja.es/servlet/oaites?codigo=141 |
| work_keys_str_mv |
AT inarrealasherasmanuel metododemelnikovbandasdeestocasticidadynointegrabilidadenungirostatoconmomentosdeinerciavariables |
| _version_ |
1718346548795932672 |