论文标题
在周期性扰动的限制三体问题中的过境轨道的几何形状
Geometry of transit orbits in the periodically-perturbed restricted three-body problem
论文作者
论文摘要
在循环限制的三体问题中，通过对沿线拉格朗格点的管理微分方程进行线性化来揭示低能传输轨道。当考虑时间周期性扰动时，此过程将失败，例如由于太阳引起的扰动（即双圆形问题）或原始轨道偏心。对于时间周期性扰动的情况，拉格朗日点被周期性轨道取代，该轨道等效地被视为符号映射的双曲线纤维纤维固定点（Stroboscocicpoincaré映射）。可以在关于固定点的离散图中确定过境和非传输轨道，类似于连续动力学系统中关于Index-1鞍均平衡点的几何结构。此外，尽管连续的时间系统不能保存哈密顿能量（这是随着时间变化的），但线性化的映射本地保存了与时间无关的有效汉密尔顿功能。我们证明了从不受干扰到定期扰动的情况，它可以保留到运输和非透射轨道的相位空间几何形状，后者将其延伸到完整的非线性方程。
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are considered, such as perturbation due to the sun (i.e., the bicircular problem) or orbital eccentricity of the primaries. For the case of a time-periodic perturbation, the Lagrange point is replaced by a periodic orbit, equivalently viewed as a hyperbolic-elliptic fixed point of a symplectic map (the stroboscopic Poincaré map). Transit and non-transit orbits can be identified in the discrete map about the fixed point, in analogy with the geometric construction of Conley and McGehee about the index-1 saddle equilibrium point in the continuous dynamical system. Furthermore, though the continuous time system does not conserve the Hamiltonian energy (which is time-varying), the linearized map locally conserves a time-independent effective Hamiltonian function. We demonstrate that the phase space geometry of transit and non-transit orbits is preserved in going from the unperturbed to a periodically-perturbed situation, which carries over to the full nonlinear equations.
