Document Type

Conference Paper

Journal/Book Title/Conference

40th Annual AAS Guidance & Control Conference

Location

Breckenridge, CO

Publication Date

2017

First Page

1

Last Page

14

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

Abstract

The Clohessy-Wiltshire equations are commonly used to describe the relative orbit motion of two spacecraft in proximity to each other. The relative motion solution provided by these equations is most naturally given in a local-vertical, local horizontal frame. However, if a nearby spacecraft is spinning in a controlled or uncontrolled manner, it may be more convenient to describe the relative orbital motion in the rotating spacecraft-fixed frame. This may be especially true for satellite inspection or approach to a spinning spacecraft. In this paper a set of linear-time-varying differential equations describing the orbital relative motion of two spacecraft as observed from a rotating spacecraft-fixed frame are developed. It is shown that when the spacecraft is rotating with the LVLH frame (i.e., nadir pointing spacecraft), these differential equations reduce to the standard Clohessy-Wiltshire equations, as expected. Additionally, it is shown that these equations also become linear-time-invariant if the spin rate of the rotating spacecraft is much greater than the orbital rate (which is generally small). In this case, a closed-form solution for the spacecraft-relative motion and associated transition matrix is obtained. The analytic state-transition matrix is conveniently used to develop a simple targeting algorithm for operations in the vicinity of a spinning spacecraft. This is shown to be useful when a transfer from one spacecraft-relative position to another spacecraft-relative position is desired. Some simple targeting and trajectory optimization examples are provided.

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