{"id":114557,"date":"2018-03-11T10:42:36","date_gmt":"2018-03-11T10:42:36","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-el-satelite-en-rotacion-rapida-comparacion-forma-cerrada-vs-desarrollos\/"},"modified":"2018-03-11T10:42:36","modified_gmt":"2018-03-11T10:42:36","slug":"sobre-el-satelite-en-rotacion-rapida-comparacion-forma-cerrada-vs-desarrollos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/ciencias-de-la-tierra-y-del-espacio\/sobre-el-satelite-en-rotacion-rapida-comparacion-forma-cerrada-vs-desarrollos\/","title":{"rendered":"Sobre el sat\u00e9lite en rotaci\u00f3n r\u00e1pida. comparaci\u00f3n forma cerrada vs. desarrollos"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Francisco Javier Molero Madrid <\/strong><\/h2>\n<p>Resumen en castellano  esta memoria aborda el estudio de la din\u00e1mica de actitud de un s\u00f3lido r\u00edgido triaxial (parte integrable) bajo la acci\u00f3n de lo que se conoce como gravity-gradient torque (perturbaci\u00f3n). El sistema as\u00ed constituido resulta ser uno de los modelos b\u00e1sicos no integrables v\u00e1lidos para analizar el movimiento tanto de sat\u00e9lites artificiales como de otros cuerpos naturales.  una forma muy com\u00fan de abordar este tipo de problemas es llevar a cabo lo que se conoce como la reducci\u00f3n completa de la parte integrable considerada como orden cero. En ese sentido se han propuesto en la literatura distintos conjuntos de variables tomando como base las variables de andoyer. As\u00ed, el principal objetivo de este trabajo es mostrar el comportamiento de dos conjuntos diferentes de estas variables que pueden presentar ciertas propiedades que las hacen m\u00e1s o menos adecuadas para el estudio de una perturbaci\u00f3n. El primer conjunto, conocido como variables de \u00e1ngulo-acci\u00f3n, fue introducido por sadov, el cual ser\u00e1 comparado con un nuevo conjunto propuesto recientemente por ferrer y lara.  adem\u00e1s del cap\u00edtulo introductorio, en el cap\u00edtulo 2 se realiza una revisi\u00f3n del s\u00f3lido libre. La integraci\u00f3n del problema no perturbado se da en variables de andoyer, las cuales se emplear\u00e1n para llevar a cabo la reducci\u00f3n completa del problema. Por otra parte, este cap\u00edtulo 2 recoge en detalle la idea de llevar a cabo la integraci\u00f3n del problema realizando una regularizaci\u00f3n consistente en un cambio de la variable independiente (el tiempo). En ambas integraciones se ofrecen detalles sobre la manipulaci\u00f3n de las funciones el\u00edpticas involucradas. El cap\u00edtulo finaliza con una secci\u00f3n donde se recoge el estudio de las fases del problema.  el cap\u00edtulo 3 muestra c\u00f3mo se lleva a cabo la reducci\u00f3n completa del problema resolviendo la ecuaci\u00f3n de hamilton-jacobi a la poincar\u00e9. Dado que existen distintas variables intermedias que permiten resolver las cuadraturas existentes, utilizamos una diferente a la propuesta por sadov para deducir un conjunto alternativo de variables de \u00e1ngulo-acci\u00f3n cuya bondad depender\u00e1 del tipo de perturbaci\u00f3n que se est\u00e9 manejando. Finalmente se presentan las ecuaciones de transformaci\u00f3n expresadas en t\u00e9rminos de funciones theta de jacobi.  en el cap\u00edtulo 4 se realiza una aproximaci\u00f3n en forma cerrada de primer orden del problema perturbado donde se muestra, no s\u00f3lo el modo en que se manejan las funciones el\u00edpticas bajo el m\u00e9todo de perturbaci\u00f3n, sino tambi\u00e9n las diferencias existentes cuando \u00e9stas se analizan empleando los dos conjuntos diferentes de variables estudiados en esta memoria. A su vez, el cap\u00edtulo 5 emula al cap\u00edtulo 4 con el objetivo de comparar las soluciones anal\u00edticas y num\u00e9ricas dadas por un desarrollo en serie de la funci\u00f3n perturbaci\u00f3n. En este sentido, dado que anteriores trabajos han llevado a cabo desarrollos en serie de fourier, en esta memoria exploramos la posibilidad de llevar a cabo series de taylor de funciones el\u00edpticas previamente expresadas en t\u00e9rminos de funciones theta de jacobi.  los resultados muestran que la aplicaci\u00f3n de ambos conjuntos de variables a la perturbaci\u00f3n tratada difiere esencialmente en el hecho de que la derivada de la funci\u00f3n zeta de jacobi con respecto al m\u00f3dulo el\u00edptico, presente en las ecuaciones de transformaci\u00f3n, no es peri\u00f3dica en variables ferrer-lara, lo cual produce un efecto rizado creciente en la evoluci\u00f3n temporal de las variables del problema que no se observa en las variables de \u00e1ngulo-acci\u00f3n.   resumen en ingl\u00e9s  this memoir focuses on the attitude dynamics of a triaxial rigid body (integrable part) under gravity-gradient torque (perturbation), which is considered one of the basic nonintegrable models to analyze the attitude propagation of artificial satellites, although this approximation is also valid to describe the motion of natural bodies.  a common way to tackle such approximations is to accomplish the complete reduction of the integrable part considered as the zero order. Different sets of variables have been proposed in the literature in order to address such analytical approximation, most of them starting from andoyer variables. Thus, the main goal of this work is to show the behaviour of two different sets of these variables which may present a number of properties which can make them more or less suitable for the study of a perturbation. The first set, well known as action-angle variables, was introduced by sadov and we will compare it with a new set recently proposed by ferrer and lara.  apart from the introduction, in chapter 2 the free rigid body dynamics is revisited. The integration of the torque-free motion is given in andoyer variables, which will be used to accomplish the complete reduction of the torque-free motion. Some details on the manipulation of the involved elliptic functions are also given. Furthermore, a different way to address the integration of the free rigid body problem is carried out by a regularization of time. Finally, due to a renewal of interest in geometric aspects of the rigid body dynamics, a study of the phases of the problem is also included.  chapter 3 shows how the complete reduction is carried out by solving the hamilton-jacobi-poinca\u00e9 equation. Moreover, an alternative intermediary variable is used to build up a new set of action-angle variables which may be utilized for the study of a number of perturbations.Par  next, a first-order closed form solution of the perturbed problem is presented in chapter 4 where it is shown not only the way to handle the elliptic functions under a perturbation method but also the existing differences when analyzing them using the two different sets of variables given by sadov and ferrer-lara. In turn, chapter 5 emulates chapter 4 in order to compare the analytical and numerical solutions given by a series expansion of the perturbing function. In this sense, since other previous works have carried out expansions as fourier series, in this work we explore the possibility of developing taylor expansions of the elliptic functions previously expressed in terms of jacobi theta functions.  the results show that the application of both sets of variables to the perturbing function differs in the fact that the partial derivative of the jacobi zeta function with respect to the elliptic modulus, which is present in the transformation equations, is not periodic in ferrer-lara variables. This fact produces an increasing curly effect along the evolution of the variables of the problem which is not observed when action-angle variables are used.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre el sat\u00e9lite en rotaci\u00f3n r\u00e1pida. comparaci\u00f3n forma cerrada vs. desarrollos<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre el sat\u00e9lite en rotaci\u00f3n r\u00e1pida. comparaci\u00f3n forma cerrada vs. desarrollos <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Francisco Javier Molero Madrid <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Murcia<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 22\/07\/2013<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Sebastian Ferrer Martinez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 manuel Ferrandiz leal <\/li>\n<li>mercedes Arribas jim\u00e9nez (vocal)<\/li>\n<li>Antonio Vigueras campuzano (vocal)<\/li>\n<li>Jes\u00fas Pel\u00e1ez \u00e1lvarez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Francisco Javier Molero Madrid Resumen en castellano esta memoria aborda el estudio de la din\u00e1mica de actitud 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