The theory of asynchronous relative motion II: universal and regular solutions

详细信息    查看全文

• 作者：Javier Roa ; Jesús Peláez
• 关键词：Relative motion ; Elliptic rendezvous ; Hyperbolic rendezvous ; Kustaanheimo–Stiefel transformation ; Sperling–Burdet regularization ; Sundman transformation ; Stumpff functions
• 刊名：Celestial Mechanics and Dynamical Astronomy
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：127
• 期：3
• 页码：343-368
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Astrophysics and Astroparticles; Dynamical Systems and Ergodic Theory; Aerospace Technology and Astronautics; Geophysics/Geodesy; Classical Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9478
• 卷排序：127

文摘

Two fully regular and universal solutions to the problem of spacecraft relative motion are derived from the Sperling–Burdet (SB) and the Kustaanheimo–Stiefel (KS) regularizations. There are no singularities in the resulting solutions, and their form is not affected by the type of reference orbit (circular, elliptic, parabolic, or hyperbolic). In addition, the solutions to the problem are given in compact tensorial expressions and directly referred to the initial state vector of the leader spacecraft. The SB and KS formulations introduce a fictitious time by means of the Sundman transformation. Because of using an alternative independent variable, the solutions are built based on the theory of asynchronous relative motion. This technique simplifies the required derivations. Closed-form expressions of the partial derivatives of orbital motion with respect to the initial state are provided explicitly. Numerical experiments show that the performance of a given representation of the dynamics depends strongly on the time transformation, whereas it is virtually independent from the choice of variables to parameterize orbital motion. In the circular and elliptic cases, the linear solutions coincide exactly with the results obtained with the Clohessy–Wiltshire and Yamanaka–Ankersen state-transition matrices. Examples of relative orbits about parabolic and hyperbolic reference orbits are also presented. Finally, the theory of asynchronous relative motion provides a simple mechanism to introduce nonlinearities in the solution, improving its accuracy.