发表机构
School of Aeronautics and Astronautics, Shenzhen Campus of Sun Yat-sen University; Shenzhen Key Laboratory of Intelligent Microsatellite Constellation（中山大学深圳校区航空航天学院; 深圳市智能微小卫星星座重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对Kozai驱动抛射体，提出了适用于目标天体处于偏心倾斜轨道的碰撞频率计算方法，验证了其与特殊情况的一致性，且结果与动力学积分吻合。
AI 中文摘要
对于经历Lidov-Kozai长期演化的高倾角抛射体，其偏心率与倾角的耦合变化会使长期碰撞频率的估算变得复杂。此前针对Kozai驱动抛射体的碰撞频率研究，均假设目标天体的轨道为圆轨道或限制在参考平面内。本研究考虑了一般情况，即目标天体的轨道同时具有非零偏心率和非零倾角。对于每个完整的Lidov-Kozai周期，初始相对交点经度和目标天体的初始近心点幅角作为两个独立的方位变量，针对每对初始值计算单周期碰撞频率。在本研究考虑的不可通约条件下，通过对两个方位变量显式求平均得到长期平均值。对于目标天体轨道为圆轨道或位于参考平面内的特殊情况，该方法在解析上可简化为对应先前研究的公式，数值对比也证实了这种简化。对于一般的偏心倾斜情况，所得碰撞频率预测的抛射体存活曲线与独立直接动力学积分得到的剩余抛射体占比吻合良好。最后表明，在固定动力学设置和不可通约条件下，与给定闭合哈密顿能级曲线相关的长期平均碰撞频率，既与抛射体沿该能级曲线的初始长期状态无关，也与其初始升交点经度无关。
英文摘要
For high-inclination projectiles undergoing Lidov--Kozai secular evolution, coupled variations in eccentricity and inclination complicate estimates of long-term collision frequencies with a target body. Previous collision-frequency studies for Kozai-driven projectiles have considered target-body orbits that are either circular or confined to the reference plane. The present study considers the general case in which the target body's orbit has both non-zero eccentricity and non-zero inclination. For each complete Lidov--Kozai cycle, the initial relative nodal longitude and the target body's initial argument of periapsis serve as two independent orientation variables. The single-cycle collision frequency is evaluated for each pair of initial values. Under the incommensurability condition considered here, the long-term mean is then obtained by explicitly averaging these values over both orientation variables. For the special cases in which the target body's orbit is circular or lies in the reference plane, the method is shown analytically to reduce to the corresponding formulations of previous studies. Numerical comparisons confirm these reductions. For the general eccentric and inclined case, the resulting collision frequency predicts a projectile survival curve that agrees well with the fraction of projectiles remaining in independent direct dynamical integrations. Finally, it is shown that, for a fixed dynamical setup and under the incommensurability condition, the long-term mean collision frequency associated with a given closed Hamiltonian level curve is independent of both the projectile's initial secular state along that level curve and its initial longitude of ascending node.
Comments24 pages, 3 figures
