Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.     

The arrangement in mean elements space of the periodic orbits close to that of the Moon

In a simplified model of the Earth-Moon-Sun system based on the restricted circular 3-dimensional 3-body problem, it is possible to find numerically a set of 8 periodic orbits whose time evolutions closely resemble that of the Moon's orbit. These orbits have a period of 223 synodic months (i.e. the period of the Saros cycle known for more than two millennia as a means of predicting eclipses), and are characterized by a secular rotation of the argument of perigee . Periodic orbits of longer durations exhibiting this last feature are very abundant in Earth-Moon-Sun dynamical models. Their arrangement in the space of the mean orbital elements- for various values of the lunar mean motion is presented.     

Periodic orbits of an electric charge in a magnetic dipole field

Periodic orbits in the Stormer problem are studied using the symmetry lines of the Poincaré map introduced by De Vogelaere. Many known facts are explained by mean of these lines. The dynamics of four special symmetry lines when the Stormer parameter ₁ changes is presented, and we obtain a clear global view of the structure of the simple periodic orbits and their bifurcations, including the asymmetrical ones. New asymmetrical multiple periodic orbits are obtained.     

Investigating the propagation mechanism of unmodelled systematic errors on coordinate time series estimated using least squares

The propagation of unmodelled systematic errors into coordinate time series computed using least squares is investigated, to improve the understanding of unexplained signals and apparent noise in geodetic (especially GPS) coordinate time series. Such coordinate time series are invariably based on a functional model linearised using only zero and first-order terms of a (Taylor) series expansion about the approximate coordinates of the unknown point. The effect of such truncation errors is investigated through the derivation of a generalised systematic error model for the simple case of range observations from a single known reference point to a point which is assumed to be at rest by the least squares model but is in fact in motion. The systematic error function for a one pseudo-satellite two-dimensional case, designed to be as simple but as analogous to GPS positioning as possible, is quantified. It is shown that the combination of a moving reference point and unmodelled periodic displacement at the unknown point of interest, due to ocean tide loading, for example, results in an output coordinate time series containing many periodic terms when only zero and first-order expansion terms are used in the linearisation of the functional model. The amplitude, phase and period of these terms is dependent on the input amplitude, the locations of the unknown point and reference point, and the period of the reference point's motion. The dominant output signals that arise due to truncation errors match those found in coordinate time series obtained from both simulated data and real three-dimensional GPS data.     

天文卫星下传数据处理系统的规划

天文卫星获取的数据需要经过卫星下传数据处理系统的一系列加工,生成可以分析的数据产品,这些产品及相应软件要发布给国内外用户,同时数据处理系统还要监测载荷状态、数据质量及天体源爆发等。这样,下传数据处理系统的建设直接关系到物理成果的获取,规划该系统就变得非常有意义。从数据产品定义、子系统规划、数据流程等方面介绍卫星下传数据处理系统的规划,并提出以模块化开发方式从整体上协调各个子系统的开发,使各个系统及其软件相互配合,共同促进科学产出。     

1991年江淮梅雨暴雨与亚洲季风的关系

利用实际大气参数取值进行尺度分析，求得斜压半地转模式中非线性斜压Ｒｏｓｓｂｙ波的非频散周期解的存在条件与解。给出了能够描述非线性特性波动的无量纲拟能效ε，由此推导了非线性特征波动的波速公式及波参数间的一些诊断关系。     

短时间尺度周期性热力强迫下流型的低频振荡

本文在正压涡度方程中引进短时间尺度周期性热力强迫项。在一定的参数范围内,该强迫项可以引起环流指数准两至三周的低频振荡。     

Astronomical time scale for the Middle Oxfordian to Late Kimmeridgian in the Swiss and French Jura Mountains

Detailed investigation of facies and sedimentary structures reveals that, during the Middle Oxfordian to Late Kimmeridgian, the shallow carbonate platform of the Swiss and French Jura Mountains recorded high-frequency sea-level fluctuations quite faithfully. The cyclostratigraphic analysis within the established biostratigraphic and sequence-chronostratigraphic framework implies that the resulting hierarchically stacked depositional sequences formed in tune with the orbital cycles of precession (20 kyr) and eccentricity (100 and 400 kyr). The astronomical time scale presented here is based on the correlation of 19 platform sections and 4 hemipelagic sections from south-eastern France where good biostratigraphic control is available. The cyclostratigraphic interpretation suggests that the interval between sequence boundaries Ox4 and Kim1 (early Middle Oxfordian to earliest Kimmeridgian) lasted 3.2 myr and that the Kimmeridgian sensu gallico has a duration of 3.2 to 3.3 myr. The astronomical time scale proposed here is compared to time scales established by other authors in other regions and the discrepancies are discussed. Despite these discrepancies, there is a potential to estimate the durations of ammonite zones and depositional sequences more precisely and to better evaluate the rates of sedimentary, ecological and diagenetic processes. Editorial handling: Hanspeter Funk, Helmut Weissert, Stefan Bucher     

解析法测定天文方位角计算软件

介绍北极星时角法测定天文方位角的基本方法，进而说明解析法测定天文方位角的基本原理，阐述计算软件的功能、菜单设计特点和操作方法，以实例说明软件的实用性。