Analytic approach on geometric structure of invariant manifolds of the collinear Lagrange points  

作　　者：LU Jing WANG Qi WANG ShiMin 

机构地区：[1]School of Aeronautics Science and Engineering, Beihang University, Beijing 100191, China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2012年第9期1703-1712,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos. 10832004 and 11102006);the FanZhou Foundation (Grant No. 20110502)

摘　　要：An analytical method is proposed to find geometric structures of stable,unstable and center manifolds of the collinear Lagrange points.In a transformed space,where the linearized equations are in Jordan canonical form,these invariant manifolds can be approximated arbitrarily closely as Taylor series around Lagrange points.These invariant manifolds are represented by algebraic equations containing the state variables only without the help of time.Thus the so-called geometric structure of these invariant manifolds is obtained.The stable,unstable and center manifolds are tangent to the stable,unstable and center eigenspaces,respectively.As an example of applicability,the invariant manifolds of L 1 point of the Sun-Earth system are considered.The stable and unstable manifolds are symmetric about the line from the Sun to the Earth,and they both reach near the Earth,so that the low energy transfer trajectory can be found based on the stable and unstable manifolds.The periodic or quasi-periodic orbits,which are chosen as nominal arrival orbits,can be obtained based on the center manifold.An analytical method is proposed to find geometric structures of stable, unstable and center manifolds of the collinear La- grange points. In a transformed space, where the linearized equations are in Jordan canonical form, these invariant manifolds can be approximated arbitrarily closely as Taylor series around Lagrange points. These invariant manifolds are represented by algebraic equations containing the state variables only without the help of time. Thus the so-called geometric structure of these invariant manifolds is obtained. The stable, unstable and center manifolds are tangent to the stable, unstable and center eigen- spaces, respectively. As an example of applicability, the invariant manifolds of L1 point of the Sun-Earth system are considered The stable and unstable manifolds are symmetric about the line from the Sun to the Earth, and they both reach near the Earth, so that the low energy transfer trajectory can be found based on the stable and unstable manifolds. The periodic or qua- si-periodic orbits, which are chosen as nominal arrival orbits, can be obtained based on the center manifold.

关 键 词：analytical method stable manifold unstable manifold center manifold geometric structure 

分 类 号：O561.1[理学—原子与分子物理] TP271[理学—物理]