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

Kostantinos Papadakis  Constantine Goudas 《Astrophysics and Space Science》2006,305(2):99-124

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.  相似文献   

多接收器电感耦合等离子体质谱法测定镉标准溶液中镉的同位素组成   总被引：1，自引：1，他引：0  

高博  梁细荣  刘颖  胡光黔  曾文  涂湘林 《岩矿测试》2008,27(5):321-324

建立了多接收器电感耦合等离子体质谱仪对Cd标准溶液同位素组成进行分析的实验方法。仪器的质量分馏校正采用Standard-Sample Bracketing法。实验结果用δ114/110Cd来表达。在此研究基础上,以SPEX Cd标准溶液为参考标准,对国外4种Cd标准溶液进行了测定。结果表明,实验测定的精度在0.07‰~0.13‰(δ114/110Cd),与目前文献报道的结果具有相似的精度。以最新SPEX Cd标准样品(δ114/110Cd=0)为基准,计算的δ114/110CdJMC、δ114/110CdSPEX-1、δ114/110CdBAM1012和δ114/110CdM櫣nster的值分别为0.55‰、0.56‰、-0.65‰和5.14‰,说明不同批次SPEX标准溶液的Cd同位素组成是明显不同的,最新的SPEX Cd标准溶液与SPEX-1 Cd的δ114/110Cd值存在着0.56‰的差别。将以SPEX Cd为参考标准的δ114/110CdBAM1012和δ114/110CdM櫣nster转化为以SPEX-1或JMC为参考标准后,得到的结果与文献报道的结果在误差范围内一致。  相似文献   

滇西北保山核桃坪铅锌矿床成矿流体来源的同位素地球化学证据   总被引：11，自引：2，他引：9  

薛传东  韩润生  杨海林  杨志明  田世洪  刘勇强  郝百武 《矿床地质》2008,27(2):243-252

滇西北核桃坪铅锌矿是保山地块内沿澜沧江断裂带发育的一个大型铅锌多金属矿床,矿体严格受近SN向的断裂带及层间破碎带控制,赋存于上寒武统核桃坪组和沙河厂组大理岩化灰岩及矽卡岩中。文章在分析矿床地质特征的基础上,通过对V1矿体的氢、氧、碳、硫、硅和铅同位素地球化学的示踪研究,探讨了成矿溶液中水、碳、硅、硫和铅的来源以及成矿流体的演化问题。研究表明,V1矿体中矿石的石英δ18O水值变化范围为6·1‰~7·6‰,平均为6·7‰,其δDV-SMOW值变化范围为-100‰~-108‰,平均为-104‰,说明成矿流体主要来自深部岩浆分异水,并在后期成矿作用过程中有地层建造水和大气降水的加入;矿石中方解石的δ13CV-PDB和δ18O水值分别为-6·6‰~-5·9‰和5·0‰~5·2‰,反映成矿流体的碳、氧具有深部流体与围岩发生交代反应的特征。硅、硫和铅同位素具深部岩浆或地幔来源的特点,但遭受后期壳源物质的混染。据此提出该矿床是与深部岩浆热液或幔源流体贯入有关的构造热液脉型矿床,其成矿作用受控于深部过程的驱动和控制,可为指导地质找矿提供依据。  相似文献   

基于Poulos弹性理论的被动桩改进算法     

陈福全  黄伟达 《岩土力学》2008,29(4):905-910

传统的Poulos弹性理论仅适合于均质土中土体侧向位移时桩的性状分析,无法考虑土的层状特性。通过引入层状地基中作用一水平集中力的广义Mindlin解和地面作用有竖向荷载时的应力和位移通解,对Poulos方法进行了改进,使之扩展到多层土中,还用于研究堆载条件下的被动桩变形和受力响应。算例分析表明,改进弹性理论要比Poulos方法更为严密、合理,提高了计算精度,应用范围也更广。  相似文献   

Modelling of periodic wave transformation in the inner surf zone     

P. Bonneton   《Ocean Engineering》2007,34(10):1459-1471

In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement.  相似文献   

水溶液中聚合物在粘土上的吸附          下载免费PDF全文

王修林 《海洋与湖沼》1993,24(4):420-427

水溶液中聚合物在粘土上的吸附对于聚合物污染防治和污水处理等都有重要意义。Scheutjens-Fleer理论是应用范围最广的聚合物吸附理论,适应于从单体到长链高聚物,从链无相互作用的稀溶液到纯聚合物的吸附研究。本文简要介绍了有关聚合物吸附的重要参数,包括吸附量、耦合分数或直接表面覆盖、平均层厚度和链段密度,以及相应的测定方法。文中分析了影响聚合物吸附研究发展的主要问题,指出水溶液中聚合物在粘土上的吸附研究的发展方向是综合研究吸附等温线和A/V效应、耦合分数、吸附层厚度、吸附分级现象和对粘土层间的影响,并与Scheutjens-Fleer理论计算结果进行比较。  相似文献   

南海尖峰海山多金属结壳地球化学   总被引：4，自引：5，他引：4  

梁宏锋  姚德  刘新波  梁德华 《海洋地质与第四纪地质》1991,(4)

南海尖峰海山多金属结壳富含30多种元素,其锰铁矿物主要由钡镁锰矿,δ-MnO_2和FeOOH·xH_2O组成。与其它海区的结壳相比,尖峰海山结壳富含Cu、Ni、Ba、Zn、Pb等元素,而Co、Ti、稀土元素(REE)、Sr等元素相对较贫。研究表明,HREE亏损,具明显的Ce正异常,较明显的Tb正异常和Yb负异常。这是氧化弱碱性海洋环境所致。结壳是水成作用的产物,它的形成受南海独特的古海洋环境所控制,海底火山热液作用,可能也是影响因素之一。  相似文献   

冲绳海槽中段沉积岩芯碳酸盐和烧失量的古环境意义     

吴世迎  刘焱光  王湘芹  白黎明  吴军瑞 《海洋科学进展》2001,19(2):17-24

对冲绳海槽中段 3个沉积岩芯碳酸盐和烧失量的系统分析得知 ,岩芯沉积物的CaCO3含量一般 >1 0 % ,最高含量接近 30 % ,烧失量大都在 1 0 %～ 30 %之间变化 ,反映了该海区处于溶跃面之上钙质生物极为发育的生物地球化学环境。结合δ1 8O曲线所反映的气候环境变化 ,探讨了 1 2 0kaB .P .以来碳酸盐旋回的“大西洋型”演变特点 ,同时对该区沉积地层中的火山热液活动印记作了一定的探讨。  相似文献   

漳州地区热田的水热活动及其成因   总被引：1，自引：0，他引：1  

柯龙生 《台湾海峡》1997,16(1):21-27

本文通过漳州地热田及其周围地区的水热活动、地质构造特征及人工爆破、重力、地磁、电性结构、地震活动性等综合地球物理场之间关系分析，得出漳州地热田是高热异常背景下产生的对流型水热系统：深切到上地幔的ＮＥ向长乐－南澳断裂、ＮＷ向九龙江断裂及Ｅ－Ｗ向南靖－厦门断裂控制了地下水的深循环，使大气降水得以下渗到〉３ｋｍ深度，被地温加热并富集起来，在静水压力作用下沿通道－断裂带的交汇部位上涌。热田区破碎的岩石导致  相似文献   

A perturbation solution for nonlinear structural response to oscillatory flow     

A.W. Lipsett   《Applied Ocean Research》1986,8(4):183-189

  相似文献