Formation design in elliptical orbit using relative orbit elements |
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| Affiliation: | 1. Department of Mathematics, Eastern Connecticut State University, Willimantic, CT 06226, United States;2. Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609, United States;1. Deutsches Zentrum für Luft- und Raumfahrt (DLR), German Space Operations Center (GSOC), Münchner Str. 20, 82234 Wessling, Germany;2. University at Baffalo (SUNY) and Consultant, Vineyard Haven, MA, USA;3. Head GNSS Technology and Navigation Group, DLR/GSOC, 82234 Wessling, Germany;4. Head Space Situational Awareness Group, DLR/GSOC, 82234 Wessling, Germany;1. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia;2. Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk, 71491, Saudi Arabia;1. School of Engineering, Faculty of Engineering and Built Environment, University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia;2. NTIS–New Technologies for the Information Society, Faculty of Applied Sciences, University of West Bohemia, Technická 8, 306 14, Plzeň, Czech Republic;3. School of Earth and Planetary Sciences, Curtin University of Technology, GPO Box U1987, Perth, WA, 6845, Australia |
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| Abstract: | A new set of relative orbit elements is strictly defined through spherical geometry. The exact transformation equations between the new relative orbit elements and classical-orbital elements are derived. A new relative motion model with no singularity problem is derived based on the relative orbit elements, which are suitable for both elliptical and circular reference orbits. The in-plane and out-of-plane relative motion can be completely decoupled based on the new model. The inverse transformation of state transfer matrix is obtained to analyze perturbation effects and control strategy. The geometric characteristics of relative motion can be easily described using the relative eccentricity/inclination vector method. The proposed method and conclusions are validated by simulation through some typical examples. This paper improves the basic theory of relative orbit elements and unifies the expressions of the elliptical and near-circular close relative motion. |
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