Amplitude Condition

Author: Tianjiang Shuo

Website: https://cislunarspace.cn

Definition

The nonlinear coupling constraint between the in-plane amplitude Ax and out-of-plane amplitude Az in the circular restricted three-body problem, determined by fixed coefficients l₁, l₂, and Δ in the Richardson analytical framework, expressed as l₁Ax² + l₂Az² + Δ = 0. This condition ensures the third-order approximate solution remains periodic; Ax and Az are not independent parameters but must satisfy this quadratic constraint. When the amplitude combination departs from the amplitude condition, the orbit degenerates into an unclosed Lissajous-type trajectory.

Application Value

幅值condition l₁Ax² + l₂Az² + Δ = 0 确保 Halo orbit三阶近似解maintain周期性. 当振幅组合偏离幅值conditionWhen , orbit退化for 非闭合 of Lissajous 型轨迹.

References

  • Halo轨道的航天器编队构型设计
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