Artificial satellites orbits in 2:1 resonance: GPS constellation |
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Authors: | JC Sampaio AGS Neto SS Fernandes R Vilhena de Moraes MO Terra |
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Institution: | 1. UNESP-Univ Estadual Paulista, CEP. 12516-410 Guaratinguetá-SP, Brazil;2. ITA-Inst Tecnológico de Aeronáutica, 12228-900 São José dos Campos, SP, Brazil;3. UNIFESP-Univ Federal de São Paulo, 12231-280 São José dos Campos, SP, Brazil |
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Abstract: | 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. |
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