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Master's Dissertation
DOI
10.11606/D.45.2011.tde-23072012-133230
Document
Author
Full name
Marcelo Farias Caetano
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2011
Supervisor
Committee
Garcia, Manuel Valentim de Pera (President)
Mello, Sylvio Ferraz de
Ragazzo, Clodoaldo Grotta
Title in Portuguese
Estabilidade vertical no problema circular de Sitnikov
Keywords in Portuguese
estabilidade
movimentos periódicos
problema de sitnikov
Abstract in Portuguese
Estudamos um caso especial do problema restrito dos três corpos, chamado problema circular de Sitnikov, quando dois corpos de massas iguais (chamadas de primárias) estão em uma órbita circular (configuração central de dois corpos), enquanto que um terceiro corpo de massa negligenciada (chamada infinitesimal) oscila sobre uma reta perpendicular ao plano das primárias (chamaremos esse movimento de vertical periódico). Aqui analisamos a estabilidade desse movimento periódico, com relação a pequenas perturbações nas direções ortogonais a reta onde ocorre o movimento. Chamaremos a atenção ao fenômeno de alternância entre estabilidade e instabilidade na família do movimento periódico vertical, conforme variamos a amplitude do movimento.
Title in English
On vertical stability in Sitnikov problem
Keywords in English
Periodic Motions
Sitnikov Problem
Stability
Abstract in English
We studied a special case of the restricted three-body problem, named circular problem of Sitnikov, when two body of equal mass (called primaries) moving around each other on circular motion (central configuration of two body), while the third body of negligible mass (called infinitesimal) performs along a straight line orthogonal to the plane of the primaries (so called periodic vertical motions). We analyze the stability of the periodic vertical motions with respect to small perturbations orthogonal to the straight line where the motions occurs. We call attention to the phenomenom of alternation of stability and instability within the family of periodic vertical motions, whenever their amplitude is varied in a continuous manner.
 
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mestrado.pdf (1.03 Mbytes)
Publishing Date
2012-08-13
 
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