论文标题
关于椭圆限制的三体问题的光环轨道和光晕管的分析构造
On the analytical construction of halo orbits and halo tubes in the elliptic restricted three-body problem
论文作者
论文摘要
空间循环限制的三体问题的光环轨道在太空飞行动力学中被大大考虑，以设计天体之间的低能传递。用于计算光环轨道的非常有效的分析方法，以及相关转移，是从Lagrangian Points L1-L2定义的高阶Birkhoff正常形式获得的。在本文中，通过实施非线性浮动式伴侣共鸣正常形式，我们提供了轨道的定义及其歧管管，它们在椭圆形三体问题的近似值中存在，并将圆形问题的光环概括。由于此类光环轨道的库幅度很大（与L1-L2与次级体的距离相当），并且Birkhoff正常形式是通过Lagrangian Points在Lagrangian Point的串联膨胀中获得的，我们还提供了与真正的椭圆形限制三体问题的轨道相对于该方法的误差分析。
The halo orbits of the spatial circular restricted three-body problem are largely considered in space-flight dynamics to design low-energy transfers between celestial bodies. A very efficient analytical method for the computation of halo orbits, and the related transfers, has been obtained from the high-order resonant Birkhoff normal forms defined at the Lagrangian points L1-L2. In this paper, by implementing a non-linear Floquet-Birkhoff resonant normal form, we provide the definition of orbits, as well as their manifold tubes, which exist in a large order approximation of the elliptic three-body problem and generalize the halo orbits of the circular problem. Since the libration amplitude of such halo orbits is large (comparable to the distance of L1-L2 to the secondary body), and the Birkhoff normal forms are obtained through series expansions at the Lagrangian points, we provide also an error analysis of the method with respect to the orbits of the genuine elliptic restricted three-body problem.
