Other
Scientific paper
Oct 1981
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981cemec..25..111h&link_type=abstract
Celestial Mechanics, vol. 25, Oct. 1981, p.111-136.
Other
16
Attitude Stability, Gravitational Effects, Orbital Mechanics, Perigees, Satellite Orbits, Satellite Perturbation, Angular Momentum, Control Stability, Eccentricity, Lunar Gravitation, Satellite Attitude Control, Solar Gravitation, Trajectory Analysis, Zonal Harmonics
Scientific paper
An improved theory is presented of long period perigee motion for orbits near the critical inclinations 63.4 and 116.6 deg. Inclusion of lunisolar perturbations and all measured zonal harmonic coefficients from a recent earth model are significant improvements over existing theories. Phase portraits are used to depict the interaction between eccentricity magnitude and argument of perigee. The Hamiltonian constant can be chosen as the parameter to display a family of phase plane trajectories consisting of libration, circulation, and asymptotic motion along separatrices near equilibrium points. A two parameter family of phase portraits is defined by the other two integrals, the average semimajor axis and component of angular momentum resolved along the earth's polar axis. There are regions of the parameter space where the stability and the total number of equilibria can change, or two separatrices can coalesce. These phenomena signal large qualitative changes in phase portrait topology. Numerical studies show that lunisolar perturbations control stability of equilibria for orbits with semimajor axes exceeding 1.4 earth radii. Moreover, a theory which includes lunisolar perturbations predicts larger maximum fluctuations in eccentricity and faster oscillations near stable equilibria compared to a theory which models only the zonal harmonics.
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