Investigation of Spin-Orbit Resonance about a Semi-Synchronous Near Polar Orbit.

摘要

An investigation of the spin-orbit resonance effects for a semi-synchronous near polar orbit was undertaken in order to determine whether consideration of all resonance terms associated with a particular commensurability ratio would result in the existence of multiple equilibrium points for placement of satellites utilizing this type of orbit. The Hamiltonian of the geopotential in Delaunay elements using first and second order zonal harmonic terms was first transformed to a set of modified variables. The effects of the resonant disturbing function were then developed and the resultant Hamiltonian, valid for near polar inclinations and small eccentricities, was reduced to a single degree of freedom through a second transformation. Phase portraits of the system Hamiltonian were then generated and an analysis of the resonance structure and librational periods performed. A single equilibrium point for each resonance term was discovered. Because of the physical meaning of the critical argument, the stable equilibrium points for both the first and second resonance terms appear to be candidates for deployment of future satellite systems. The semi-analytic technique of phase potraits was shown to be a feasibile approach to the investigation of resonance effects.