Poincaré Mapping

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A dimensionality-reduction technique for analyzing continuous dynamical systems. By recording the successive intersections of a trajectory with a chosen cross-section in phase space, the continuous flow is reduced to a discrete map. The pattern of mapped points reveals whether orbits are periodic, quasi-periodic, or chaotic. In low-energy transfer design, an extended Poincaré mapping uses two sections (e.g., a lunar orbit section and an L2 exit section) to convert continuous manifold trajectories into discrete inter-section correspondences, facilitating the search for energy-optimal escape orbits.

Application Value

This term在cislunar space missions中has important application value. In orbit design, it can be used foroptimizing transfer trajectories, reducing mission fuel consumption. In attitude control and dynamics analysis, it helps understandthe motion characteristics of spacecraft in complex gravitational fields, providing theoretical support for mission planning. In navigation and orbit determination, methods based on this termcan improve orbit prediction accuracy, supporting the development of autonomous navigation algorithms.

Related Concepts

• Periodicity Conditions in Relative Orbital Motion
• Helix Formation
• Energy Dissipation Method
• Unstable Manifold

References

• 荆武兴和刘玥 - 2014 - 椭圆三体问题下月球L2低能逃逸轨道设计