Mathematics – Dynamical Systems
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........19s&link_type=abstract
Ph.D. Thesis Michigan Univ., Ann Arbor.
Mathematics
Dynamical Systems
7
Dynamic Models, Dynamical Systems, Equations Of Motion, Gas Giant Planets, Planetary Rings, Spacecraft Motion, Artificial Satellites, Fine Structure, Mission Planning, Solar System
Scientific paper
The theory of planetary rings is the subject of much study recently, due to the discovery of rings around all the gas giant planets in the Solar System. Most of these studies focus on explaining the fine structure of rings and on modeling specific observed phenomenon. Starting from a classical model for rings, a new model for satellite motion is derived which accounts for the gravitational attraction of the ring. This model has application to spacecraft motion near a ring, mission planning considerations, and to the natural dynamics of ring growth and stability. Specifically, the use of symmetric central configurations to study selected issues of planetary ring dynamics was investigated. Classical stability results for symmetric central configurations are reconsidered and improved. The dynamics of satellites with infinitesimal mass attracted by a class of symmetric central configurations are investigated and a new and original dynamical model for satellite motion is derived. Fundamentals of this model are studied, including Hill stability, invariant transformations, equilibrium points and their stability, and periodic orbits. Rigorous approximations to this model are introduced for different geometries. When the satellite is far from the ring, the dynamical model may be reduced to a set of integrable equations. When the satellite is close to the ring, a simplified set of non-integrable equations are found, these equations are a generalization of Hill's equations of motion applied to the case of a planetary ring. A family of periodic orbits is also derived which describes the regular motion of a satellite about a ring. Several results from the new dynamical models are discussed. Among them are a self-limiting mechanism for a planetary ring to gain mass and a derivation of the general orbit of a satellite in the presence of a ring. Future applications of the dynamical models derived are discussed. These applications apply to artificial satellites, mission planning, and natural ring dynamics.
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