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@PhDThesis{Mateus:2022:DiPaRe,
               author = "Mateus, Dairo Antonio Cuellar",
               school = "Instituto Nacional de Pesquisas Espaciais (INPE)",
         englishtitle = "Dynamincs of a particle in teseral resonance with the homogeneous 
                         triaxial ellipsoid",
              address = "S{\~a}o Jos{\'e} dos Campos",
                 year = "2022",
             keywords = "astrodin{\^a}mica, resson{\^a}ncia, perturba{\c{c}}{\~o}es 
                         orbitais, harm{\^o}nicos esf{\'e}ricos, sistemas hamiltonianos, 
                         astrodynamics, resonance, orbital perturbation, spherical 
                         harmonics, hamiltonian system.",
           targetfile = "publicacao.pdf",
            committee = "Carvalho, Francisco das Chagas (presidente) and Prado, 
                         Ant{\^o}nio Fernando Bertachini de Almeida (orientador) and 
                         Sanchez, Diogo Merguizo (orientador) and Moraes, Rodolpho Vilhena 
                         de and Terra, Maisa de Oliveira and Domingos, Rita de 
                         C{\'a}ssia",
                month = "2022-08-02",
             abstract = "A din{\^a}mica de uma part{\'{\i}}cula em resson{\^a}ncia 
                         tesseral ao redor de um elipsoide triaxial homog{\^e}neo {\'e} 
                         analisada neste trabalho. Esta resson{\^a}ncia resulta da 
                         comensurabilidade entre o spin do corpo e o movimento m{\'e}dio 
                         da {\'o}rbita. Como caso de estudo, analisaremos a din{\^a}mica 
                         de uma part{\'{\i}}cula na {\'o}rbita da resson{\^a}ncia 
                         tesseral 3:1 no planeta an{\~a}o Haumea. Esta {\'o}rbita {\'e} 
                         de nosso interesse por se encontrar na regi{\~a}o do anel de 
                         poeira que circunda esse planeta an{\~a}o. N{\'o}s propomos 
                         quatro modelos da anisotropia do corpo prim{\'a}rio e analisamos 
                         a sua din{\^a}mica resultante por meio da formula{\c{c}}{\~a}o 
                         hamiltoniana e pelo m{\'e}todo das equa{\c{c}}{\~o}es 
                         planet{\'a}rias de Lagrange. Comparando os resultados obtidos 
                         nessas duas abordagens, observamos que o modelo reduzido da 
                         anisotropia domina a din{\^a}mica da part{\'{\i}}cula nas 
                         {\'o}rbitas estudadas. Ap{\'o}s isto, analisamos as 
                         resson{\^a}ncias tesserais 2:1 e 3:1 no elipsoide triaxial 
                         homog{\^e}neo em equil{\'{\i}}brio hidrost{\'a}tico ou 
                         elipsoide de Jacobi. Nele, determinamos os pontos singulares, 
                         centro e pontos de sela, das duas resson{\^a}ncias e mostramos 
                         que esses pontos n{\~a}o dependem da quantidade de massa do corpo 
                         prim{\'a}rio. Neste corpo, determinamos o seu per{\'{\i}}odo de 
                         rota{\c{c}}{\~a}o e a localiza{\c{c}}{\~a}o das {\'o}rbitas 
                         ao redor dele. Segundo nosso estudo, os asteroides Ida e Chariklo 
                         s{\~a}o identificados como elipsoides de Jacobi no Sistema Solar. 
                         ABSTRACT: The dynamics of a particle in tesseral resonance around 
                         a homogeneous triaxial ellipsoid is analyzed in this work. This 
                         resonance results from the commensurability between the spin of 
                         the body and the mean motion of the orbit. As a case study, we 
                         will analyze the dynamics of a particle in the orbit of the 
                         tesseral resonance 3:1 on the dwarf planet Haumea. This orbit is 
                         of interest to us because is located in the region of the Haumeas 
                         dust ring. We propose four models for the primary body anisotropy 
                         and analyze their dynamics using the Hamiltonian formulation and 
                         the Lagrange planetary equations method. Comparing the results 
                         obtained in these two approaches, we observed that the reduced 
                         anisotropy model dominates the particle dynamics in the orbits 
                         studied. Also, we analyzed the 2:1 and 3:1 tesseral resonances on 
                         the homogeneous triaxial ellipsoid in hydrostatic equilibrium or 
                         Jacobi ellipsoid. Using this body, we determine the singular 
                         points, center and saddle points, of the two resonances and we 
                         show that these points do not depend on the amount of mass of the 
                         primary body. In this body, we determine its period of rotation 
                         and the location of orbits around it. According to our study, the 
                         asteroids Ida and Chariklo are identified as Jacobi ellipsoid in 
                         equilibrium in the solar system.",
                title = "Din{\^a}mica de uma part{\'{\i}}cula em resson{\^a}ncia 
                         tesseral com o elipsoide triaxial homog{\^e}neo",
                  ibi = "8JMKD3MGP3W34T/479GT5E",
                  url = "http://urlib.net/ibi/8JMKD3MGP3W34T/479GT5E",
                pages = "103",
             language = "pt",
        urlaccessdate = "05 out. 2022"
}


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