New State Transition Matrix for Formation Flying in J(2)-Perturbed Elliptic Orbits

作者：Yamada Katsuhiko^*; Kimura Masaya; Shima Takeya; Yoshikawa Shoji

来源：Journal of Guidance, Control, and Dynamics, 2012, 35(2): 536-547.

DOI：10.2514/1.53926

A state transition matrix for formation flying in eccentric orbits is considered in this paper. The relative motion of the formation flying obeys the Tschauner-Hempel equations, which are extended for the presence of a J(2) perturbation. Furthermore, the state transition matrix of the Tschauner-Hempel equations is extended for J(2), and it is demonstrated that the extended state transition matrix becomes the solution of the extended Tschauner-Hempel equations. Because the extended state transition matrix only uses osculating orbital elements in the initial state and does not use mean orbital elements, an analytical treatment of the state transition matrix is possible. When the state transition matrix uses only the first-order term of J(2), the errors sometimes become large compared with the relative distance multiplied by J(2) in a time range that is longer than one orbit period. A method to suppress errors numerically is also proposed.

• 出版日期2012-4