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Dynamical systems: an integrable kernel for resonance effects

doi: 10.6062/jcis.2009.01.02.0009(Free PDF)


Jorge Kennety S. Formiga and Rodolpho Vilhena de Moraes


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.


Resonance, artificial satellites, celestial mechanics, dynamics systems.


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