On The Concept Of Periapsis In Hill’s Problem

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.     

Structures in the phase space of a four dimensional symplectic map

We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence.     

Minor planet short periodic perturbations: The indirect part of the disturbing function

Leverrier's development of the indirect part of the disturbing function has been extended to include terms up to degree 4 in eccentricity and inclination; the resulting series has been expressed with respect to a fixed plane, and in a computer readable form (a list of integers). Tests have been performed for the relative significance of the terms of degrees 2, 3 and 4, and estimates have been obtained for the accuracy of the short periodic perturbations of a minor planet, and of the corresponding mean orbital elements. It was found that: (i) even in extreme cases, the indirect part of the disturbing function gives rise to very small short periodic perturbations; (ii) bodies of very high eccentricity/inclination and those close to mean motion resonances are most significantly affected; (iii) indirect perturbations for minor planets can be computed up to the degree 2 terms only, without any significant loss of accuracy; and (iv) higher degree indirect perturbations appear to be important only for their contribution to the long periodic effects of higher order (with respect to the perturbing mass).     

The Homoclinic Tangle of A 1:2 Resonance in a 2-D Hamiltonian System

We study in great detail the geometry of the homoclinic tangle, with respect to the energy, corresponding to an unstable periodic orbit of type 1:2, on a surface of section representing a 2-D Hamiltonian system. The tangle consists of two resonance areas, in contrast with the tangles of type-l or -{l, m, k, x = 0} considered in previous studies, that consist of only one resonance area. We study the intersections of the inner and outer lobes of the same resonance area and of the two resonance areas. The intersections of the lobes follow certain rules. The detailed study of these rules allows us to derive quantitative relations about the number of intersections and to understand the complex behavior of the higher order lobes by studying the lower order lobes. We find 1st, 2nd, 3rd, etc. order intersections formed by lobes making 1, 2, 3, etc. turns around an island. After a sufficiently high order of iterations a lobe may intersect its image and thus produce a Poincaré recurrence. Numerical results for a wide interval of energies are presented. The number of intersections changes through tangencies. In any finite interval of the energy between two tangencies of 1st order, an infinite number of higher order tangencies occur and thus, according to the Newhouse theorem, there exist nearby islands of stability.     

Resonant Periodic Orbits of Trans-Neptunian Objects

We study two and three-dimensional resonant periodic orbits, usingthe model of the restricted three-body problem with the Sun andNeptune as primaries. The position and the stability character ofthe periodic orbits determine the structure of the phase space andthis will provide useful information on the stability and longterm evolution of trans-Neptunian objects. The circular planarmodel is used as the starting point. Families of periodic orbitsare computed at the exterior resonances 1/2, 2/3 and 3/4 withNeptune and these are used as a guide to select the energy levelsfor the computation of the Poincaré maps, so that all basicresonances are included in the study. Using the circular planarmodel as the basic model, we extend our study to more realisticmodels by considering an elliptic orbit of Neptune and introducingthe inclination of the orbit. Families of symmetric periodicorbits of the planar elliptic restricted three-body problem andthe three-dimensional problem are found. All these orbitsbifurcate from the families of periodic orbits of the planarcircular problem. The stability of all orbits is studied. Althoughthe resonant structure in the circular problem is similar for allresonances, the situation changes if the eccentricity of Neptuneor the inclination of the orbit is taken into account. All theseresults are combined to explain why in some resonances there aremany bodies and other resonances are empty.     

珠江三角洲网河区水位变化趋势研究

根据珠江三角洲网河区29个验潮站的实测验潮记录,应用傅氏变换与最平滤波器串联的方法来消除月均序列的周期波动对确定水位变化趋势的影响,由低通序列一元线性回归分析确定各站水位的变化趋势;结果表明,周期波动对确定海平面变化趋势的影响是显著的.应用经验正交函数(EOF)对网河区的水位变化场进行分解,由相互独立的时间函数和空间特征函数表征网河区区域的水位变化特征;应用时间特征函数计算区域水位的平均变化率为0.02mm/a.根据验潮站的水位变化趋势,探讨网河区水位变化与河床冲淤的关系.     

一类广义Sine-Gordon方程的概周期解

用最大值原理和Banach压缩映像原理研究一类广义Sine-Gordon方程的概周期解问题,证明概周期解的存在‖u‖L∞<π2中的唯一性。     

2021年10月山西一次罕见持续性强降水过程物理机制分析

利用气象观测资料、NCEP/NCAR 1°×1°再分析资料以及GDAS资料,对2021年10月2-7日山西持续性强降水天气过程进行分析。结果表明：稳定的乌拉尔山低槽后部冷空气扩散,中纬度短波槽东移,与副热带高压外围西南暖湿气流持续交汇,同时高低空急流耦合形成强烈上升运动,低层切变线和地面辐合线稳定维持,及低层水汽不断输送并形成辐合,为持续性强降水的发生发展提供有利动力和水汽条件。此次强降水过程分为对流性降水和稳定性降水2个阶段,2阶段水汽输送通道的源地、路径、高度均有明显差异,但水汽输送贡献率均以对流层中低层山西南侧的水汽输送占主导地位。降水开始前,对流层中上层存在对称不稳定,大气可降水量明显跃增;对流性降水阶段,干空气不断入侵,对流不稳定快速建立与释放,对流层中低层水汽辐合区与强上升气流配合,导致山西出现强对流天气。地形的阻挡、抬升及地形收缩作用,对局地极端强降水具有增幅作用。     

Periodic orbits and their bifurcations in a 3-D system

We study some simple periodic orbits and their bifurcations in the Hamiltonian . We give the forms of the orbits, the characteristics of the main families, and some existence diagrams and stability diagrams. The existence diagram of the family 1a contains regions that are stable (S), simply unstable (U), doubly unstable (DU) and complex unstable (). In the regionsS andU there are lines of equal rotation numberm/n. Along these lines we have bifurcations of families of periodic orbits of multiplicityn. When these lines reach the boundary of the complex unstable region, they are tangent to it. Inside the region there are linesm/n, along which the orbits 1a, describedn-times, are doubly unstable; however, along these lines there are no bifurcations ofn-ple periodic orbits. The families bifurcating from 1a exist only in certain regions of the parameter space (, ). The limiting lines of these regions join at particular points representing collisions of bifurcations. These collisions of bifurcations produce a nonuniqueness of the various families of periodic orbits. The complicated structure of the various bifurcations can be understood by constructing appropriate stability diagrams.