地球-月球系统中近矩形双星轨道的有效稳定性
Effective Stability of Near-Rectilinear Halo Orbits in the Earth-Moon System
AI总结：
研究地球-月球系统中近矩形双星轨道的动力学稳定性，通过离散Poincaré映射和多项式正则形式，推导出Nekhoroshev型估计，揭示其非线性约束特性。
摘要：
近矩形双星轨道（NRHOs）在圆限制三体问题（CR3BP）中表现出复杂的动力学景观，特征是嵌套在强不稳定性区域内的正常椭圆轨道带。这种稳定与不稳定动力学的共存，由于月球附近轨道的数值敏感性而更加复杂。理解这些椭圆轨道的有效稳定性是关键挑战，涉及局部正则形式理论和全局不稳定性机制的交集。为量化有限时间约束，我们构建了有效稳定性严谨框架，利用jet传输计算高阶泰勒展开，构造显式多项式正则形式。通过识别规范化阶数，推导出离散Nekhoroshev型估计，平衡映射解析域的渐近收敛性与低阶小除数的累积惩罚。将此框架应用于地球-月球系统，将所得几何极限直接映射到物理空间坐标。关键发现是，对于实际任务寿命（如10-50年），所需稳定性远短于特征Nekhoroshev积累时间。因此，有效稳定性区域不受时间依赖指数漂移限制，而是由优化正则形式的最大解析域完全决定。这些推导的空间包络建立了内在局部稳定性的几何边界，为CR3BP中非线性约束提供了严谨的数学描述。
英文摘要：
Near-rectilinear halo orbits (NRHOs) around Earth-Moon L2 in the Circular Restricted 3-Body Problem (CR3BP) exhibit a complex dynamical landscape, featuring a band of normally elliptic orbits embedded within regions of strong instability. This coexistence of stable and unstable dynamics, amplified by the numerical sensitivity associated with close lunar passages, makes the long-term behavior of trajectories near NRHOs a delicate and intrinsically nonlinear problem. Understanding the effective stability of these elliptic orbits is therefore a critical challenge, lying at the intersection of local normal form theory and global instability mechanisms. To quantify finite-time confinement, we formulate a rigorous framework for effective stability using discrete Poincaré maps. By employing jet transport to compute high-order Taylor expansions, we construct explicit polynomial normal forms. We derive discrete Nekhoroshev-type estimates by identifying the normalization order, which balances the asymptotic convergence of the map's analyticity domain against the cumulative penalty of low-order small divisors. Applying this framework to the Earth-Moon system, we map the resulting geometric limits directly into physical spatial coordinates. Crucially, we demonstrate that for practical mission lifetimes (e.g., 10-50 years), the required stability is vastly shorter than the characteristic Nekhoroshev accumulation time. Consequently, the effective stability region is not constrained by the time-dependent exponential drift, but is instead governed entirely by the maximum analytical domain of the optimized normal form. These derived spatial envelopes establish explicit geometric boundaries for the intrinsic local stability of elliptic NRHOs, providing a rigorous mathematical characterization of their nonlinear confinement within the CR3BP.
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