Artificial satellites orbits in 2:1 resonance: GPS constellation

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• 作者：J.C. Sampaio^a ; ^{jarbascordeiro@gmail.com} ; A.G.S. Neto^b ; ^{artur2304@yahoo.com.br} ; S.S. Fernandes^b ; ^{sandro@ita.br} ; R. Vilhena de Moraes^c ; ^{rodolpho.vilhena@gmail.com} ; M.O. Terra^b ; ^maisa@ita.br
• 关键词：Artificial satellites ; Resonance ; Orbits
• 刊名：Acta Astronautica
• 出版年：2012
• 出版时间：December, 2012
• 年：2012
• 卷：81
• 期：2
• 页码：623-634
• 全文大小：2428 K

文摘

In this work, the resonance problem in the artificial satellites motion is studied. The development of the geopotential includes the zonal harmonics J₂₀ and J₄₀ and the tesseral harmonics J₂₂ and J₄₂. Through an averaging procedure and successive Mathieu transformations, the order of dynamical system is reduced and the final system is solved by numerical integration. In the simplified dynamical model, three critical angles are studied. The half-width of the separatrix is calculated through a linearized model which describes the behavior of the dynamical system in a neighborhood of each critical angle. Through the resonance overlap criterion the possible regular and irregular motions are investigated by the time behavior of the semi-major axis, argument of perigee and eccentricity. The largest Lyapunov exponent is used as tool to verify the chaotic motion.