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95/105= 0.91


1,1

Dynamical systems: an integrable kernel for resonance effects

doi: 10.6062/jcis.2009.01.02.0009(Free PDF)

Authors

Jorge Kennety S. Formiga and Rodolpho Vilhena de Moraes

Abstract

A suitable sequence of canonical transformations reduces the system of differential equations describing the orbital motion to an integrable dynamic system. Through this dynamic system, the motion of an artificial satellite subject to geopotential perturbations and resonances between the frequencies of the mean orbital motion and the Earth rotational motion is analyzed. The behavior of the motion of the satellite is analyzed in the neighborhood of the 2:1 resonances. The phase space of the resulting system is studied considering that one resonant angle is fixed. Simulations are presented showing the time-behavior of the semi-major axis of artificial satellites.

Keywords

Resonance, artificial satellites, celestial mechanics, dynamics systems.

References

[1] BELETSKII VV. 1975. Resonance Phenomena at Rotations of Artificial and Natural Celestial Bodies. In: GIACAGLIA GEO (Ed). Satellites dynamics. Berlin. Verlang.

[2] CELESTRAK. 2004. "NORAD 2-line Elements". 10 Ago. 2004, .

[3] FERRAZ MELO S. 1979. Periodic orbits in a region of instability created by independent small divisors. In: NAGOZY E & FERRAZ MELO S (Eds). Natural and artificial satellite motion. Austin: University of Texas Press, p. 283-292.

[4] FORMIGA JKS. 2005. Estudo de ressonâncias no movimento orbital de satélites artificiais. 2005. 133f. Dissertação (Mestrado em Física) - Faculdade de Engenharia do Campus de Guaratingueta, Universidade Estadual Paulista, Guaratingueta, São Paulo, Brazil.

[5] HAMILL PJ & BLITZER L. 1974. Spin-orbit coupling: a unified theory of orbital and rotational resonance. Celestial mechanics, 9: 127-146. 10.1007/BF01236168

[6] HUGUES S. 1980. Earth satellite Orbits with Resonant Lunisolar Perturbations. Resonances dependent only inclination. Proceedings of the Royal society of London serie A. London, 372(1745): 243-264.

[7] LIMA Jr. PHCL. 1998. Sistemas ressonantes a altas excentricidades no movimento de satelites artificiais. Tese (Doutorado em 1998), Instituto tecnológico de aeronáutica, São José dos Campos, São Paulo, Brazil.

[8] OSORIO JP. 1973. Perturbações de orbitas de satélites no estudo do campo gravitacional terrestre. Porto: Imprensa Portuguesa.

[9] VILHENA DE MORAES R & SILVA PAF. 1990. Influence of the resonance in gravity-gradient stabilized satellite. Celestial mechanics and dynamical astronomy, 47: 225-243. 10.1007/BF00053453

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