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.     

Seagrass landscape-scale changes in response to disturbance created by the dynamics of barrier-islands: A case study from Ria Formosa (Southern Portugal)

This study documents long-term changes of a Zostera noltii landscape induced by a natural cyclic event in a coastal lagoon. The barrier-islands forming this system are very dynamic with drifting movements controlling ecological patterns and processes occurring in this area. Changes in the areal extent of the Z. noltii meadows were assessed using historical aerial photographs from 1940, 1980, 1989, 1996 and 1998. Landscape indices such as total patch area (TA), mean patch size (MPS), number of patches (NP), mean shape coefficient of variation (CV) and landscape fractal dimension (D) were calculated for each year and related to an index of disturbance intensity. The spatial distribution of the Z. noltii meadows varied greatly during the studied period and changes observed were related to the disturbance created by the barrier-islands' spatial dynamics. After an artificial inlet relocation the Z. noltii area, number of patches, patch mean size and coefficient of variation decreased. The fractal dimension of the Z. noltii landscape increased by 50% showing that besides a decrease in total area, number of patches, and patch mean area, patch fragmentation was an important consequence of this anthropogenic disturbance.Seagrass natural distribution patterns changed in response to natural and human-induced activities. This study emphasizes the importance of the landscape approach and the historical perspective when studying seagrass changes and the importance of taking into consideration long-term changes in seagrass landscapes to avoid confusion between man-induced effects with natural cyclic events.     

Infinitesimal orbits around lagrange points in the elliptic,restricted three-body problem

This study presents a method of obtaining asymptotic approximations for motions near a Lagrange point in the planar, elliptic, restricted three-body problem by using a von Zeipel-type method. The calculations are carried out for a second-order escape solution in the proximity of the equilateral Lagrange point, L ₄, where the primaries' orbital eccentricity is taken as the small parameter .     

山东月湖的沉积物分布特征及搬运趋势

1998年 11～ 12月和 1999年 8～ 9月各一个月对月湖进行的野外工作 ,共取得表层沉积物样品 131个 ,应用激光粒度仪并结合传统的筛分法对这些样品进行粒度分析 ,进行矩法计算获得粒度参数。采用Gao命名方法 ,将沉积物划分出 5种主要类型。利用Gao -Collins粒径趋势分析模型 ,计算该区沉积物粒径趋势所显示的沉积物净搬运方向 ,结果表明 ,沉积物从四周向湖中心搬运 ,同时显示湾顶的西部和北部、涨潮三角洲以及湖心等地貌单元是沉积的优势区域。     

A variance-ratio test for supporting a variable mean in kriging

This article discusses the issue of whether to use a variable mean and describes a test that can be used to evaluate whether it is justified to add terms to the drift (deterministic part) of a geostatistical model. The basic model could be the intrinsic one, where the deterministic part is a constant, and the alternate model could be any model that includes a constant term in the expression for the drift. Also, differences between constant- and variable-mean models are discussed.     

基于受限汉语的GIS路径重建研究

主要研究基于自然语言 (汉语 )的GIS路径重建问题 ,通过分析带有路径表述信息的汉语文本 ,建立了汉语的NLRP句法模型 ,它是由带有空间语义的动作以及作为动作对象的地理要素构成的集合。考虑到自然语言理解实现的需求 ,论文基于NLRP句法模型定义了受限汉语的NLRP文法 ,在此基础上 ,描述了路径重建算法PRA ,并探讨了算法实现中由于空间认知原因带来的不确定性问题以及其解决方案。最后 ,基于该算法进行了相关实例研究 ,从而验证了该算法的正确性     

海南博螯沿岸地貌与人类活动的潜在影响

The Boao coastal system along the eastern coast of Hainan Island is a dynamic delta-tidal inlet-barrier formed during the late Holocene. The delta developed inside a shallow lagoon barred by a sandy barrier with a narrow, shallow tidal inlet opening. Two major distributary channels separated by small islands characterize the delta. The lagoon is silting up receiving and trapping sediments from both the river and, in minor measure during storms, through the tidal inlet opening and barrier washovers. The barrier at the tidal inlet is highly dynamic and changes its form, accreting (migrating spit) against the inlet during fair-weather conditions and being eroded during storms and river floods.The delta has almost completely filled the lagoon and major concerns exist on the effect that ongoing large development plans may have on the environment. These concerns include the effect on floods and rate of siltation once banks of the islands have been stabilized and floodwater and sediment load are impeded from spreading over the lowlands, and the effect of increasing pollutant loads from the new facilities on the ecosystems of the increasingly restricting lagoon water and on the seashores.     

Development and Extension of An Aggregated Scale Model: Part 1 – Background to ASMITA

Whilst much attention has been given to models that describe wave, tide and sediment transport processes in sufficient detail to determine the local changes in bed level over a relatively detailed representation of the bathymetry, far less attention has been given to models that consider the problem at a much larger scale (e.g. that of geomorphological elements such as a tidal flat and tidal channel). Such aggregated or lumped models tend not to represent the processes in detail but rather capture the behaviour at the scale of interest. One such model developed using the concept of an equilibrium concentration is the Aggregated Scale Morphological Interaction between Tidal basin and Adjacent coast (ASMITA). In this paper we provide some new insights into the concepts of equilibrium, and horizontal and vertical exchange that are key components of this modelling approach. In a companion paper, we summarise a range of developments that have been undertaken to extend the original model concept, to illustrate the flexibility and power of the conceptual framework. However, adding detail progressively moves the model in the direction of the more detailed process-based models and we give some consideration to the boundary between the two.     

潟湖潮汐通道水力特性与治理

综合论述了潟湖潮汐通道口门之流速、断面面积、通道长度、延时角和饱满系数之间的关系,以及沿岸漂沙对口门的影响。对不同类型的潟湖潮汐通道,提出了中潮位射流导流堤、口门复式断面和通道分汊等治理方法及其通道口门相关尺度的具体计算。