Classical Exponential Sinusoid

Author: Tianjiang Shuo Website: https://cislunarspace.cn

Definition

The original form of the exponential sinusoid shape function: r = k0 exp[k1 sin(k2 θ + φ)], proposed by Petropoulos and Longuski for low-thrust trajectory design in the two-body framework. In the CR3BP, this formulation is acceptable for closer transfers (below GEO altitude) but insufficient where the gravity of both primaries is comparable.

Application Value

形状法利用解析函数近似轨迹几何形状，为高精度的最优控制求解器提供良好的初始猜测，是小推力转移轨道设计的重要工具。

References

• Vellutini & Avanzini, 2014, Shape-based design of low-thrust trajectories to cislunar lagrangian point