Sliding Rule

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

A method for determining optimal initial and terminal coasting durations by sliding along contours on a cost map. Given the initial separation angle and total transfer time, allowing coasting shifts the sampling point on the contour plot: initial coasting moves along a line with slope 1/(ω1-ω2), while terminal coasting slides along a vertical line. Reaching a local minimum on the contour identifies the optimal coasting duration. This paper extends the concept from Lawden's necessary conditions for primer vector theory into a practical tool for finding globally optimal solutions.

Application Value

The Sliding Rule plays a significant role in cislunar space mission design, analysis, and control. In orbital design, it can be leveraged for transfer trajectory optimization; in navigation and control, it improves mission execution precision and reliability; in system analysis, it facilitates deeper understanding of complex multi-body dynamical behavior, guiding mission planning and risk assessment.

  • J2-Invariant Orbit
  • Interior Point Optimization
  • N-Body Dynamics
  • Start-End State Constraint

References

  • Shen和Tsiotras - 2003 - Optimal two-impulse rendezvous using multiple-revolution lambert solutions
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