The general solution of the HENON–HEILES problem

The general solution of the Henon–Heiles system is approximated inside a domain of the (x, C) of initial conditions (C is the energy constant). The method applied is that described by Poincaré as ‘the only “crack” permitting penetration into the non-integrable problems’ and involves calculation of a dense set of families of periodic solutions that covers the solution space of the problem. In the case of the Henon–Heiles potential we calculated the families of periodic solutions that re-enter after 1–108 oscillations. The density of the set of such families is defined by a pre-assigned parameter ε (Poincaré parameter), which ascertains that at least one periodic solution is computed and available within a distance ε from any point of the domain (x, C) for which the approximate general solution computed. The approximate general solution presented here corresponds to ε = 0.07. The same solution is further improved by “zooming” into four square sub-domain of (x, C), i.e. by computing sufficient number of families that reduce the density parameter to ε = 0.003. Further zooming to reduce the density parameter, say to ε = 10⁻⁶, or even smaller, although easily performable in both areas occupied by stable as well as unstable solutions, was found unnecessary. The stability of all members of each and all families computed was calculated and presented in this paper for both the large solution domain and for the sub-domains. The correspondence between areas of the approximate general solution occupied by stable periodic solutions and Poincaré sections with well-aligned section points and also correspondence between areas occupied by unstable solutions and Poincaré sections with randomly scattered section points is shown by calculating such sections. All calculations were performed using the Runge-Kutta (R-K) 8th order direct integration method and the large output received, consisting of many thousands of families is saved as “Atlas of the General Solution of the Henon–Heiles Problem,” including their stability and is available at request. It is concluded that approximation of the general solution of this system is straightforward and that the chaotic character of its Poincaré sections imposes no limitations or difficulties.     

Surveying co-located space-geodetic instruments for ITRF computation

A new and comprehensive method is presented that can be used for estimating eccentricity vectors between global positioning system (GPS) antennas, doppler orbitography and radiopositioning integrated by satellites (DORIS) antennas, azimuth-elevation (AZ-EL) very long baseline interferometry (VLBI) telescopes, and satellite laser ranging (SLR) and lunar laser ranging (LLR) telescopes. The problem of reference point (RP) definition for these space-geodetic instruments is addressed and computed using terrestrial triangulation and electronic distance measurement (EDM) trilateration. The practical ground operations, the surveying approach and the terrestrial data processing are briefly illustrated, and the post-processing procedure is discussed. It is a geometrically based analytical approach that allows computation of RPs along with a rigorous statistical treatment of measurements. The tight connection between the geometrical model and the surveying procedure is emphasized. The computation of the eccentricity vector and the associated variance–covariance matrix between an AZ-EL VLBI telescope (with or without intersecting axes) and a GPS choke ring antenna is concentrated upon, since these are fundamental for computing the International Terrestrial Reference Frame (ITRF). An extension to RP computation and eccentricity vectors involving DORIS, SLR and LLR techniques is also presented. Numerical examples of the quality that can be reached using the authors approach are given. Working data sets were acquired in the years 2001 and 2002 at the radioastronomical observatory of Medicina (Italy), and have been used to estimate two VLBI-GPS eccentricity vectors and the corresponding SINEX files.     

基于球面六边形网格系统的空间信息处理方法

利用球面离散网格系统管理全球海量空间信息是一种受到普遍关注的新途径.文中提出的方法首先采用施奈德等积多面体投影将平面多分辨率六边形网格映射到球面构成网格系统;然后通过边界点四元组将球面六边形网格之间的空间关系转化为球面三角四叉树处理,利用扩展的QTM编码方案在3轴离散网格坐标系下实现了经纬度和单元地址码之间的转换;最后提出了单元分析和检索算法.实验结果表明,这种数据处理方法直接对单元地址编码进行操作,具有较高的效率.     

茂名城区GPS拟合高程精度的探讨

GPS控制网在联测水准点的基础上,利用GPS水准高程来实现GPS网点的大地高向正常高转换,其精度主要受所拟合的似大地水准面、已知点高程和GPS网点大地高3种误差的影响。     

一种基于嫦娥一号CCD影像的影像匹配方法

月球测绘是完成月球探测任务的基础保障。这里提出了一种适合于CE-1获取的CCD影像的多尺度约束自动匹配方法。首先利用SURF算子提取影像上特征点;然后进行基于准核线和最小欧式距离约束的影像匹配;最后采用随机采样算法对误匹配点进行剔除而得到同名点信息。实验结果表明,该匹配方法提取的同名点有利于CE-1月球影像DEM的生成。     

一种基于多分辨率拓扑网络的高质量初始图斑对象生成方法

本文设计一种基于多分辨率拓扑网络的拓扑启发式影像分割算法,并对其涉及关键性技术进行探讨。通过细致分割实验,验证了采用该分割算法生成高质量图斑对象的可行性。     

无地面控制点条件下卫星摄影测量的发展与现状

无地面控制点条件下, 卫星摄影测量研究与工程实践是世界各国在该领域中所面临的研究难点之一。本文介绍了在无地面控制条件下光学卫星摄影测量的研究发展和工程实践历程, 并对中国“天绘一号”卫星获取的影像实测结果进行分析, 结果表明, 中国在无地面控制条件下的卫星摄影测量研究与工程实践已居于国际领先地位。     

Effect of perturbations on the non linear stability of triangular points in the restricted three-body problem with variable mass

The effect of small perturbations ε and ε ^′ in the Coriolis and the centrifugal forces, respectively on the nonlinear stability of the triangular points in the restricted three-body problem with variable mass has been studied. It is found that, in the nonlinear sense, the triangular points are stable for all mass ratios in the range of linear stability except for three mass ratios, which depend upon ε, ε ^′ and β, the constant due to the variation in mass governed by Jeans’ law.     

Artificial halo orbits for low-thrust propulsion spacecraft

We consider periodic halo orbits about artificial equilibrium points (AEP) near to the Lagrange points L ₁ and L ₂ in the circular restricted three body problem, where the third body is a low-thrust propulsion spacecraft in the Sun–Earth system. Although such halo orbits about artificial equilibrium points can be generated using a solar sail, there are points inside L ₁ and beyond L ₂ where a solar sail cannot be placed, so low-thrust, such as solar electric propulsion, is the only option to generate artificial halo orbits around points inaccessible to a solar sail. Analytical and numerical halo orbits for such low-thrust propulsion systems are obtained by using the Lindstedt Poincaré and differential corrector method respectively. Both the period and minimum amplitude of halo orbits about artificial equilibrium points inside L ₁ decreases with an increase in low-thrust acceleration. The halo orbits about artificial equilibrium points beyond L ₂ in contrast show an increase in period with an increase in low-thrust acceleration. However, the minimum amplitude first increases and then decreases after the thrust acceleration exceeds 0.415 mm/s². Using a continuation method, we also find stable artificial halo orbits which can be sustained for long integration times and require a reasonably small low-thrust acceleration 0.0593 mm/s².