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Doctoral Thesis
DOI
10.11606/T.45.2016.tde-23082016-155031
Document
Author
Full name
Lucas Ruiz dos Santos
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2015
Supervisor
Committee
Ragazzo, Clodoaldo Grotta (President)
Mello, Luis Fernando de Osório
Mello, Sylvio Ferraz de
Michtchenko, Tatiana Alexandrovna
Salomão, Pedro Antonio Santoro
Title in Portuguese
Efeitos dissipativos em mecânica celeste modelados por corpos pseudo-rígidos
Keywords in Portuguese
Corpo pseudo-rígido
Força de maré
Sistema dissipativo
Abstract in Portuguese
O presente trabalho dedica-se a uma modelagem da interação entre corpos celestes, em regime Newtoniano, levando-se em consideração as influências que suas deformações e viscosidades internas exercem sobre seus movimentos orbitais e suas velocidades angulares. A abordagem adotada é uma variação do conhecido problema do corpo pseudo-rígido, a qual simplifica drasticamente a determinação dos equilíbrios relativos e torna a questão da dinâmica matematicamente acessível. Com este tratamento, podemos relacionar ou comparar os resultados com aqueles estabelecidos na literatura, dentre eles: formato de equilíbrio de um fluido isolado em rotação, deformação de maré causada pela interação gravitacional e o torque de maré induzido no mesmo. Pela simplicidade do modelo pode-se ainda fazer uma análise qualitativa da dinâmica do sistema e obter estimativas sobre a velocidade com que se aproxima dos equilíbrios.
Title in English
Dissipative Effects in Celestial Mechanics modeled by pseudo-rigid bodies
Keywords in English
Dissipative system
Pseudo-rigid body
Tidal force
Abstract in English
The present work is devoted to model the interaction among celestial bodies, in a Newtonian regime, but considering the role played by the internal deformation and viscosity on the orbital motion and angular velocities of the components of the system. The work is mainly developed with an alternative approach to the pseudo-rigid body model, which simplifies the determination of the relative equilibria and allows precise conclusions about the dynamics. So, we are able to compare the results of this theory with those established in the literature, namely: the equilibrium shape of an isolated fluid in rotation, the tidal elongation induced by gravitational interaction and the tidal torque. Due to its simplicity, we can further perform a qualitative analysis of the dynamics of the system and estimate the velocity of attraction of the equilibrium states.
 
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Publishing Date
2016-09-20
 
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