This paper addresses theoretical analysis of the error of TH equations with respect to relative motion equations based on Keplerian orbits. By solving a second-order integral inequality, we derive a bound function of the error. The bound function depends on initial true anomaly, initial state error, eccentricity of target orbit, and current true anomaly. Using this result, we can easily calculate the moment of impulse for correction in a multi-impulsive elliptical rendezvous based on TH equations so as to guarantee the terminal relative position and velocity errors in certain ranges. The proposed result is also illustrated by simulations of elliptical rendezvous.
On the Bound of Tschauner-Hempel Equations’ Error with Respect to Keplerian Motion
2014
Aufsatz (Zeitschrift)
Englisch
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