地月低能转移的发生条件及轨迹构造
The occurrence conditions and trajectory constructions for low energy cislunar transfers
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摘要: 应用平动点理论研究了地月低能转移的发生条件和轨迹构造. 由于空间双圆模型存在周期性扰动，传统的平动点概念不再适用；根据Hill瞬时边界的连接情况定义了等效平动点LL_{1}和LL_{2}. 通过构造合适的Poincaré截面以获得所有可能的月球捕获轨道的近月距和偏心率分布，从而获得了完全不同于Hill和圆型限制性三体问题的月面捕获能量. 在空间双圆模型下，平动点和Halo轨道不变流形的渐近结构遭到破坏：到达或离开平动点的时间，由无穷转变为有限值；运动方向由双向变为单向. 经由LL_{1}点穿越获得了最小能量的低能转移，借助LL_{1}-Halo轨道穿越得到了(M,N)-圈穿越轨道，经由LL_{2}点穿越获得了最小能量的弱稳定边界转移，借助LL_{2}-Halo轨道穿越得到了弱稳定边界逃逸和捕获窗口. 最后，以地月转移和大幅值逆行轨道的切入为例，给出低能转移的小推力、脉冲和弱稳定边界等转移的实现方式.
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关键词:
- 平动点 /
- Halo轨道 /
- 地月低能转移轨道 /
- SBCM模型 /
- Hamiltonian系统
Abstract: The paper deals with the occurrence conditions andtrajectory constructions for low-energy transfers in the cislunar space,from the views of libration point theories and nonlinear dynamicaltechniques. The classical concept of ``libration'' is unavailable forspatial bicircular model (SBCM) because of the time-dependent perturbations.So the equivalent equilibrium is defined according to the geometry ofinstantaneous Hill's boundary, i.e., LL_{1} or LL_{2}. The altitudes ofperiapsis and eccentricities of all the lunar capture trajectories arepresented via the Poincare map, and the minimum energy to capture on thelunar surface is deduced which is quite different from ones obtained incircular restricted three-body problem (CR3BP) and Hill Models. Theasymptotical behaviors of invariant manifolds flown from libration point orHalo orbit are destroyed by SBCM: the durations flown in and out of thelibration point or Halo orbit have shifted from infinite to finite, and thedirections have changed from reversible to nonreversing. The minimum energycislunar transfer is acquired by the trajectory transiting LL_{1} point,and the (M,N)- loopy transiting trajectories are attained by transitingLL_{1}-Halo orbits. Similarly, the minimum energy of weak stabilityboundary (WSB) transfer is induced by the trajectory transitingLL_{2} point, and the earth's escape and lunar capture windows for WSBtransfers are yielded by transiting LL_{2}-Halo orbits. All threetransfer manners, as low-thrust,impulse and WSB, are applied to the transfer from Earth to Moon and theinsertion of the distant retrograde orbit (DRO).-
Keywords:
- libration point /
- Halo orbit /
- low energy cislunar transfer /
- SBCM /
- Hamiltonian system
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