高倾角共振小天体长期演化的哈密顿模型  

A Hamiltonian model for the long-term evolution of high-inclination resonant small bodies

作　　者：张名艺 雷汉伦[1,2] ZHANG MingYi;LEI HanLun(School of Astronomy and Space Science,Nanjing University,Nanjing 210023,China;Key Laboratory of Modern Astronomy and Astrophysics,Ministry of Education,Nanjing 210023,China)

机构地区：[1]南京大学天文与空间科学学院,南京210023 [2]现代天文与天体物理教育部重点实验室,南京210023

出　　处：《中国科学:物理学、力学、天文学》2025年第2期121-133,共13页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家重点基础研究发展计划(编号:2019YFA0706601);国家自然科学基金(编号:12073011,1223303)资助项目。

摘　　要：平运动共振中的长期动力学对太阳系主带小天体和木星特洛伊小天体的长期动力结构具有重要影响.本文在圆型限制性三体模型框架下,建立了适用于高倾角共振小天体的半解析动力学模型,并基于绝热不变性近似,得到一个近可积哈密顿系统.在给定哈密顿量的基础上,绘制绝热不变量的相图,并将其与数值积分轨道进行了对比.对于非1:n共振和逆行1:1共振小天体,相图与数值轨道在较大范围的偏心率空间中吻合较好;而对于顺行1:1共振小天体,相图预测仅适用于高偏心率的情况.相图中的轨线为偏心率、轨道倾角和近点角距的长期动力学演化提供了全局图像,并指出了可能产生混沌的区域.将半解析模型应用于3:2共振、2:1共振、顺行1:1共振和逆行1:1共振的真实小天体,并将相图与椭圆型限制性三体系统中的积分轨迹进行对比,发现木星偏心率引起的长期摄动对高倾角3:2和2:1共振小天体的影响较小.The long-term dynamics of mean motion resonance significantly influence the dynamical structure of the main belt asteroids and the Jupiter Trojans. In this study, we establish a semi-analytical dynamical model for high-inclination resonantsmall bodies within the framework of the circular restricted three-body problem. Utilizing the adiabatic invariance approximation, we derive a nearly integrable Hamiltonian system. Based on the Hamiltonian, we construct phase diagramsof the adiabatic invariants and compare them with numerical integration trajectories. For non-1:n resonant and retrograde1:1 resonant small bodies, the phase diagrams align well with numerical orbits across a broad range of eccentricity space.Conversely, for prograde 1:1 resonant small bodies, the phase diagram predictions are valid for high eccentricity scenarios.The trajectories in the phase diagrams provide a global view of the long-term dynamical evolution of eccentricity, orbitalinclination, and argument of periapsis, highlighting potential regions of chaos. By applying the semi-analytical model toreal small bodies in the 3:2, 2:1, prograde 1:1, and retrograde 1:1 resonances, we compare the phase diagrams with integraltrajectories from the elliptical restricted three-body system. Our findings indicate that the long-term perturbations causedby Jupiter’s eccentricity have a minimal impact on high-inclination small bodies in the 3:2 and 2:1 resonances.

关 键 词：平运动共振 绝热近似 长期演化 

分 类 号：P13[天文地球—天体力学]