A methodology is proposed to design optimal time-fixed impulsive transfers in the vicinity of the L2 libration point of the Earth-Moon system, taking the construction of a space station around the collinear libration points as the background. The approximate analytical expression of motions around the L2 point in the CRTBP is given, and the expression in the ERTBP is derived by linearizing the dynamical equations for the purpose of expanding the methodology from the CRTBP to the ERTBP. Thus, the approximate analytical solution of the transfer between two points is obtained by substituting the position vectors of the two points into the expression, which solves the Lambert problem in the three-body system. Furthermore, the transfer between different orbits is constructed by parameterization of the position vectors with the amplitudes and phases of the initial orbit and the final orbit. The transfers are optimized such that the total velocity increment required to implement the transfer exhibits a global minimum. The values of variables involved in the optimal transfers are determined by the unconstrained minimization of a function of one or nine variables using a multivariable search technique. To numerically ensure that the transfers are accurate and to eliminate the linearization bias, the differential correction and SQP method are employed. The optimality of the transfers is determined lastly by the primer vector theory. Simulations of point-to-point transfers, Lissajous-to-Lissajous transfers, halo-to-halo transfers and Lissajous-to-halo transfers are made. The results of this study indicate that the approximate analytical solutions, as well as the differential correction and SQP method, are valid in the design of the optimal transfers around the libration points of the restricted three-body problem.

中文翻译：

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受限三体问题的振动点附近的最优脉冲定时传递

以在共线平衡点周围建设空间站为背景，提出了一种在地月系统L2平衡点附近设计最优定时脉冲传输的方法。给出了 CRTBP 中 L2 点附近运动的近似解析表达式，并通过将动力学方程线性化推导出 ERTBP 中的表达式，目的是将方法从 CRTBP 扩展到 ERTBP。这样，通过将两点的位置向量代入表达式，得到两点间传递的近似解析解，解决了三体系统中的Lambert问题。此外，不同轨道之间的转移是通过用初始轨道和最终轨道的幅度和相位对位置向量进行参数化来构建的。传输经过优化，以便实现传输所需的总速度增量呈现全局最小值。最优传输中涉及的变量值由使用多变量搜索技术的一个或九个变量的函数的无约束最小化确定。为了在数值上确保传输准确并消除线性化偏差，采用了微分校正和 SQP 方法。转移的最优性最后由引物矢量理论决定。进行了点对点转移、Lissajous-to-Lissajous 转移、halo-to-halo 转移和Lissajous-to-halo 转移的模拟。