Mathematics – Dynamical Systems
Scientific paper
Jun 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993jgcd...16..434w&link_type=abstract
Journal of Guidance, Control, and Dynamics (ISSN 0731-5090), vol. 16, no. 3, p. 434-440.
Mathematics
Dynamical Systems
Deimos, Dynamic Models, Orbital Mechanics, Phobos, Spacecraft Orbits, Dynamical Systems, Equations Of Motion, Hamiltonian Functions, Orbital Elements, Three Body Problem
Scientific paper
A dynamics model of a satellite of Phobos or Deimos is developed that includes Mars' gravity and oblateness and the moon's orbital eccentricity and its nonspherical shape. Two special cases of the dynamics are studied. If the moon's eccentricity is zero, then we have an autonomous system and families of periodic orbits exist. If the eccentricity is not zero, we have a time-periodic dynamical system which still permits isolated periodic orbits. The zero eccentricity periodic orbits are constructed and found to be stable at any period. In addition, the most important nonzero eccentricity period orbits are given. Sensitivity to poorly known system parameters is explored, and accuracy requirements for spacecraft insertion maneuvers are established. Stable orbits exist about both moons and are well enough known to be used by unmanned spacecraft.
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