Periapsis Poincaré Section

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A Poincaré section defined by the condition that the position vector relative to a central body is perpendicular to the velocity vector (r·v = 0) and the distance is decreasing. Unlike the traditional x-axis section, the periapsis section inherently ensures tangential velocity impulses at the section, enabling minimum-energy orbit transfers. The paper constructs separate periapsis sections centered on Earth and Moon to determine the departure and arrival points.

Application Value

In orbital design, analysis, and control, dynamics models are used to predict spacecraft trajectories, with equations of motion solved numerically or analytically. This concept underpins critical mission capabilities including orbital maneuver design, orbit improvement, and formation flying.

References

  • 郑越和赵敏 2023, §2.1
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Contributors: ouyangjiahong, Ou Yang Jiahong