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

Abdul Ahmad 《Celestial Mechanics and Dynamical Astronomy》1995,61(2):181-196

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.  相似文献   

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   

Magnetic susceptibility variations of the Edicaran cap carbonates in the Yangtze platform and their implications for paleoclimate     

吴怀春  张世红  蒋干清  李海燕 《中国海洋湖沼学报》2005,(3)

1 INTRODUCTION One of the most intriguing phenomena in the late Neoproterozoic (~750 to 543 Ma) is the globa occurrence of thin carbonates that directly overlie glacial deposits in almost every continent (Kennedy 1996; Hoffman et al., 1998; Hoffman and Schrag 2002; Brasier and Shields, 2000; James et al., 2001 Jiang et al., 2003; Nogueira et al., 2003). These “cap carbonates”, commonly several to tens of meters thick, have attracted enormous interests because o their unusually negati…  相似文献   

Discussion of de Lange, W. P. and Moon V. G. 2005. Estimating long-term cliff recession rates from shore platform widths. Engineering Geology 80, 292–301     

Wayne Stephenson   《Engineering Geology》2008,101(3-4):288-291

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On the global stratotype section and point of the Triassic base     

G. N. Sadovnikov 《Stratigraphy and Geological Correlation》2008,16(1):31-46

A unique succession of volcanogenic deposits with representative paleontological remains characterizing the Permian-Triassic boundary interval in the North Siberian platform and Taimyr is described. The succession is suitable for selecting a standard for the Triassic base in nonmarine deposits. Abundant and diverse fossils occurring in the succession evidence that volcanism responsible for origin of the plateau basalt province in Siberia was not a brief epoch of paroxysmal eruptions, which eliminated everything alive. Throughout the formation history of relevant plateau basalts, the organic world of the plateau and around existed and gradually evolved.  相似文献   

Sedimentation settings of the Vendian Vanavara formation,the Siberian platform     

B. B. Kochnev 《Stratigraphy and Geological Correlation》2008,16(1):20-30

A model of sedimentation settings is elaborated for siliciclastic deposits of the Vendian Vanavara Formation, the Katanga saddle, inner areas of the Siberian platform. Four lithologic complexes are distinguished in the formation. The lower complex is composed of proluvial continental deposits exemplifying a dejection cone of ephemeral streams. Its eroded surface is overlain by second complex largely represented by sandstones of coastal zone, which grade upward into siltstones and shales of deeper sedimentation settings (third complex). Sea transgression advanced in northeastern direction. The fourth complex resting with scouring on the third one was deposited in settings of a spacious shallow-water sea zone: in a tidal flat, sand shoals and islands. Sedimentological data are used to correlate more precisely the Vendian siliciclastic deposits of the Katanga saddle and northeastern Nepa-Botuoba anteclise, and to verify subdivision of the Vanavara Formation into subformations and character of its boundary with the overlying Oskoba Formation.  相似文献   

固定式海洋平台利用TLD的减震研究   总被引：7，自引：0，他引：7  

李宏男  马百存 《海洋工程》1996,(3)

本文研究固定式海洋平台利用调谐液体阻尼器（ＴｕｎｅｄＬｉｑｕｉｄＤａｍｐｅｒ，简称ＴＬＤ）减小地震反应的方法。首先探讨了调谐频率比、激磁频率比对减震效果的影响，在此基础上建立了ＴＬＤ——平台系统的力学模型和运动方程，通过数值计算验证了该方法的有效性  相似文献   

Long-Term Effect of TMD on Vibration Control of An MDOF Offshore Fixed Platform     

SHI  Xiang 《中国海洋工程》2003,17(4):481-494

A three-dimensional fixed offshore platform in deep water modeled by the finite element method is studied in this paper. Analysis of the dynamic response of the MDOF structure is realized taking the non-linearity of the wave drag force and the wave-structure interaction into account. The structural response statistics, which have Gaussian distributions, are used to evaluate the vibration effect of the structure without TMD and with TMD. And an optimal method to design TMD controlling the first mode of the multi-mode structure is proposed. Moreover, the probabilities of occurrence of sea states at the platform site are considered for prediction of the long-term effect of a TMD. Simulation results demonstrate that the long-term effect of a well-designed TMD is good and the practical use is possible due to the good stability of its optimal parameters under different sea states.  相似文献   

Neural Network-Based Active Control for Offshore Platforms     

周亚军  赵德有 《中国海洋工程》2003,17(3)

1 .IntroductionWiththedevelopmentofoceantechnology ,moreandmoreextremelylargeandlongflexibleoff shoreplatformsusedforoilexplorationanddrillingoperationarebuiltinhostileoceanenvironments .Ingeneral,thiskindofplatformsisanonlineardistributedparametersystemanditsnaturalfrequencyfallsclosertothedominantwavefrequencieswiththeincreaseofwaterdepth .Besides ,itsstructureisverycomplexandtheexternalwaveforceontheplatformisuncertain .Thus ,theseplatformsarepronetoexcessivewave inducedoscillationsunderbot…  相似文献   

Seismic Response Control of Offshore Platform Structures with Shape Memory Alloy Dampers     

李宏男何晓宇  霍林生 《中国海洋工程》2005,19(2):185-194

In this study, the seismic response control of offshore platform structures with Shape Memory Alloy (SMA) dampers is investigated. A new SMA damper and its restoring force medel are introduced for the calculation of seismic response reduction. Based on an actual platform structure and its mechanical medel, the parameters which may affect the rate of shock absorption are analyzed, such as the number, position and characteristics of the SMA dampers and the condition of the site where the platform is located. The results show that the SMA damper is an effective control device for offshore platforms and satisfactory control can be achieved by proper selection of the parameters.  相似文献