In this article, we perform the computation of halo orbits around libration point $L_1$ in the Sun–Jupiter system. Third-order approximation, Lindstedt–Poincare method is used to select the initial guess for libration point orbits. Furthermore, Newton’s differential correction scheme is utilized to correct the initial guess obtained from an analytical approach. Halo orbits are exceptionally unstable, the station-keeping maneuver is required to maintain the nominal halo orbit in the vicinity of collinear libration points. We have applied linear control logic in the non-linear equation of motion for the station-keeping error analysis of halo orbits and also computed the control input for halo orbits. Numerical results illustrate the viability of the proposed control technique for the exact station-keeping error at libration point $L_1$.

在本文中，我们对解放点附近的晕圈进行计算 ${\mathrm{大号}}_{\mathrm{1个}}$在太阳木星系统中。三阶近似Lindstedt-Poincare方法用于选择解放点轨道的初始猜测。此外，牛顿的差分校正方案用于校正从分析方法获得的初始猜测。晕圈非常不稳定，需要进行站台保持机动，以将名义晕圈保持在共线的解放点附近。我们在非线性运动方程中应用了线性控制逻辑，用于光环轨道的站位保持误差分析，并且还计算了光环轨道的控制输入。数值结果说明了所提出的控制技术对解放点精确站位误差的可行性。${\mathrm{大号}}_{\mathrm{1个}}$。