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

作者：Lu Jing^*; Wang Qi; Wang ShiMin

来源：Science China Physics,Mechanics & Astronomy, 2012, 55(9): 1703-1712.

DOI：10.1007/s11433-012-4810-x

• analytical method
• stable manifold
• unstable manifold
• center manifold
• geometric structure

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.

• 出版日期2012-9
• 单位北京航空航天大学