Backward Stability Set

Author: CislunarSpace

Website: https://cislunarspace.cn

Definition

The backward stability set is a concept describing motion stability when integrating the equations of motion backward in time. It is the temporal counterpart of the forward stability set. Together, forward and backward stability sets provide theoretical foundations for low-energy capture orbit design. The intersection of forward and backward stability sets identifies initial conditions that lead to bounded motion in both time directions. Li et al. applied backward stability set concepts to design ballistic capture orbits at Mars high orbits, demonstrating practical applicability for interplanetary mission design.

Key Properties

  • Computed by integrating equations of motion in reverse time direction.
  • Combined with the forward stability set to identify capture-compatible initial conditions.
  • The intersection region enables ballistic capture without dedicated insertion burns.
  • Applicable to orbit design at both Earth-Moon and planet-Sun systems.

References

  • Li, M., Zheng, J., and Meng, Y. "Ballistic Capture Orbits at Mars Based on the Backward Stability Set." Journal of Guidance, Control, and Dynamics, 2022.