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平动点附近周期轨道的不变流形因其在低能轨道转移中起着重要作用而受到广泛关注。在进行低能轨道设计的过程中不变流形要实时地进行能量匹配,但是利用传统的数值积分方法进行积分时能量会耗散。显式辛算法具有比隐式辛算法计算效率高的优势,但其要求Hamilton系统必须可以分成两个可积的部分,而旋转坐标系下的圆型限制性三体问题是不可分的,因而显式辛算法难以用于求解旋转坐标系下的圆型限制性三体问题。本文通过引入混合Lie算子,成功实现了带三阶导数项的力梯度辛算法对圆型限制性三体问题的求解,并将基于混合Lie算子的带三阶导数项的辛算法与Runge-Kutta78算法和Runge-Kutta45算法进行仿真对比,仿真结果表明基于混合Lie算子的含有三阶导数项的辛算法位置精度高、能量误差小且计算效率高。文章最后利用基于混合Lie算子的带三阶导数项的辛算法计算不变流形,可以实现低能轨道转移过程中轨道拼接点的能量精准匹配。
Invariant manifolds of periodic orbits near the translational point have drawn much attention because of their important role in low-energy orbit transfer. In the process of designing low-energy orbit, the invariant manifold needs energy matching in real time, but the energy will be dissipated when using the traditional numerical integration method. The explicit symplectic method has the advantage of higher computational efficiency than the implicit symplectic method. However, it requires that the Hamilton system must be divided into two integrable parts. However, the circular restricted three-body problem in the rotating coordinate system is inseparable, Symplectic Symplectic Algorithm is Difficult to Solve Circular Constraint Three-Body Problem in Rotation Coordinate System. In this paper, we introduce the hybrid Lie operator to solve the circular constrained three-body problem by using the force gradient symplectic algorithm with third-order derivatives. Combining the Lie algorithm with the third-order derivative term and Runge -Kutta78 algorithm and Runge-Kutta45 algorithm. The simulation results show that the symplectic algorithm based on the mixed Lie operator has the advantages of high position accuracy, small energy error and high computational efficiency. In the end, the symplectic algorithm based on the mixed Lie operator with the third derivative is used to calculate the invariant manifold, so that the energy of the orbit splitting point can be precisely matched in the process of low energy orbit transfer.