Planar Circular Restricted Three-Body Problem
Author: Tianjiang Shuo
Website: https://cislunarspace.cn
Definition
The planar simplification of the restricted three-body problem: two primaries move in circular orbits about their center of mass, the third body's mass is negligible, and its motion is constrained to the orbital plane of the primaries. Compared to the full CR3BP, PCR3BP reduces the six-dimensional phase space to four dimensions (two components each for position and velocity), simplifying analysis and computation while retaining key dynamical features including libration points, invariant manifolds, and chaos. The paper uses the Sun-Jupiter PCR3BP for studying long-time natural transport and two coupled Sun-planet PCR3BPs for short-time transport.
Application Value
The planar restricted three-body problem retains key dynamical features while reducing computational complexity, important for studying libration point orbits and natural transport mechanisms.
Related Concepts
- Variable Structure Sliding Mode Control
- Pontryagin Minimum Principle
- Error Function
References
- Ren 等 - 2011 - On the mechanisms of natural transport in the solar system
- Zhang 等 - 2020
- Topputo 2013