Nonlinear Dynamics of a Two-Chain, Three-Body Formation System
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Nonlinear Dynamics of a Two-Chain, Three-Body Formation System Ming Xu & Yan Wei & Shengli Liu
Published online: 23 July 2014 # American Astronautical Society 2014
Abstract Multibody formation constitutes a new architecture wherein the functional capabilities of a monolithic satellite are distributed, and some planned missions have begun to take advantage of the benefits offered by the use of satellite formations. The nonlinear dynamics of a two-chain, three-body formation system located on a circular orbit on the Earth is presented in this paper with the assist of nonlinear theory in astrodynamics. Different from only five libration points solved from the circular restricted three-body system, there exist sixteen equilibria for the chain system yielded by its geometry of the pseudo-potential function. For some hyperbolic equilibria, an iterative procedure is developed to correct numerically periodic orbits near them, which are referred as Lyapunov orbits in this paper. The invariant manifolds originating from those orbits are employed by Poincaré mapping to create the heteroclinic or homoclinic trajectories, and some non-transversal intersections between them are addressed in this paper. Keywords Two-chain . Formation flying . Equilibrium configuration . Lyapunov orbit . Homoclinic and heteroclinic trajectories . Poincaré mapping
Introduction Multibody formation constitutes a new architecture wherein the functional capabilities of a monolithic satellite are distributed and has attracted considerable interest, and several planned missions have been developed, such as the Terra SAR-X Add-On for Digital Elevation Measurement developed by DLR [1] and the Gravity Recovery and Climate Experiment Mission developed by ESA and NASA [2]. Compared with the classical concept involved in formation, the multibody connected system employs M. Xu (*) : Y. Wei Beihang University, Beijing 100191, China e-mail: [email protected] S. Liu China Satellite Co., Ltd., Beijing 100096, China
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J of Astronaut Sci (2012) 59:609–628
tethers or chains to join the satellites in fixing rigid configurations [3]. Benefiting from tethered or chained formations, a large number of potential flights of space tethers have been proposed lately, such as the Advanced Safety Tether Operation and Reliability Flight [4] and the Propulsive Small Expendable Deployer System [5]. Analysis of the 3D dynamics of such systems is of special interest because of motivation from the NASA research program on formation: a promising mission called Sub-millimeter Probe of the Evolution of Cosmic Structure [6] appears to be the most likely system of this kind to materialize. The orbital dynamics of the linked system of connected bodies in the gravitational field is of significant interest because of its global dynamic behavior similar to that of the classical circular restricted three-body problem (abbr. CR3BP). Initial studies on this subject were published in the early 1960s [7] and were followed by much research. The multi bodies in the connected system can general
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