New Method of the Analytic Periodic Solution for Spacecraft Formation in Elliptical Orbits
- Paper number
IAC-06-C1.5.01
- Author
Mr. Jian Jun Xing, National University of Defense Technology, China
- Coauthor
Dr. Guo-jin Tang, National University of Defense Technology, China
- Coauthor
Dr. Hai-yang Li, National University of Defense Technology, China
- Year
2006
- Abstract
Formation flying is key technology for both deep-space and orbital applications that involve multiple spacecrafts. Many future space applications will benefit from using formation flying to perform distributed observation and to provide improved coverage for surveillance. The design and evolution of the relative geometry is very important for formation flying. In this paper, an analytic method is presented to establish the periodic relative motion conditions and investigate the design approach and the evolution of the formation geometry in any elliptical reference orbits. Based on the fact of the energy equation between formation spacecrafts under the influence of a point-mass central body, necessary and sufficient conditions of periodic relative motion are presented considering the nonlinearity and eccentricity. Utilizing the presented method, we can solve not a set of nonlinear differential equations but an algebraic equation to find the two initial conditions of periodic relative motion. Using those initial conditions, formation spacecrafts could keep the periodic relative motion and could not consume any fuel onboard. The generating periodic relative motion conditions are general which do not involve any simplify assumptions except the point-mass central gravitation and fit for arbitrary values of the true anomaly of the elliptical reference orbit. Using the periodic relative motion condition as the algebraic constraint equation, the linearized differential equations of relative motion in arbitrary elliptical reference orbits could be solved simpler. Don't requiring the evaluation of a definite integral and the use of the monodromy matrix, the elegant analytic solution of periodic relative motion is developed. A great of insight could be gained from the simple analytic solution of relative motion in any elliptical orbit. These simple expressions permit the use of intuitive design methods, similar to the methods for circular orbits, to be used to specify formation parameters in eccentric orbits. Some type formations are designed. The numerical simulations verify the validity and accuracy of the proposed design method.
- Abstract document
- Manuscript document
IAC-06-C1.5.01.pdf (🔒 authorized access only).
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