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   

Chaotic Diffusion And Effective Stability of Jupiter Trojans     

Kleomenis Tsiganis  Harry Varvoglis  Rudolf Dvorak 《Celestial Mechanics and Dynamical Astronomy》2005,92(1-3):71-87

It has recently been shown that Jupiter Trojans may exhibit chaotic behavior, a fact that has put in question their presumed long term stability. Previous numerical results suggest a slow dispersion of the Trojan swarms, but the extent of the ‘effective’ stability region in orbital elements space is still an open problem. In this paper, we tackle this problem by means of extensive numerical integrations. First, a set of 3,200 fictitious objects and 667 numbered Trojans is integrated for 4 Myrs and their Lyapunov time, T_L, is estimated. The ones following chaotic orbits are then integrated for 1 Gyr, or until they escape from the Trojan region. The results of these experiments are presented in the form of maps of T_Land the escape time, T_E, in the space of proper elements. An effective stability region for 1 Gyr is defined on these maps, in which chaotic orbits also exist. The distribution of the numbered Trojans follows closely the T_E=1 Gyr level curve, with 86% of the bodies lying inside and 14% outside the stability region. This result is confirmed by a 4.5 Gyr integration of the 246 chaotic numbered Trojans, which showed that 17% of the numbered Trojans are unstable over the age of the solar system. We show that the size distributions of the stable and unstable populations are nearly identical. Thus, the existence of unstable bodies should not be the result of a size-dependent transport mechanism but, rather, the result of chaotic diffusion. Finally, in the large chaotic region that surrounds the stability zone, a statistical correlation between T_LandT_E is found.  相似文献   

CygX—1硬态高能光子的时延   总被引：1，自引：1，他引：0  

屈进禄  李惕碚 《天文学报》2001,42(2):140-147

硬X射线和软射线光子的时延时研究主能辐射的一个重要方面，傅里叶交叉谱常常被用于教育处硬软光子之间的时延，但是交叉说示能在高于30Hz的傅里叶频率上从CygX-1测量到有统计意义的快速光变，由李惕培在时域上发展的交叉相关函方法能有效测量不同时间尺度上的时延，利用此交叉相关分析方法，讨论了不同观测时期CygX-1硬态高能光子时延 的性质，分析结果表明，CygX-1硬态在短的尺度（＜0．1秒）上存存在有意义的时间延迟，并将短时间尺度上的观测结果和各种CygX-1硬态模型进行了比较讨论。  相似文献   

Distinct climate change synchronous with Heinrich event one, recorded by stable oxygen and carbon isotopic compositions in stalagmites from China   总被引：2，自引：0，他引：2  

Houyun Zhou  Jianxin Zhao  Michael K. Gagan  Jun Yan 《Quaternary Research》2008,69(2):306-315

Uranium-series dating of oxygen and carbon isotope records for stalagmite SJ3 collected in Songjia Cave, central China, shows significant variation in past climate and environment during the period 20-10 ka. Stalagmite SJ3 is located more than 1000 km inland of the coastal Hulu Cave in East China and more than 700 km north of the Dongge Cave in Southwest China and, despite minor differences, displays a clear first-order similarity with the Hulu and Dongge records. The coldest climatic phase since the Last Glacial Maximum, which is associated with the Heinrich Event 1 in the North Atlantic region, was clearly recorded in SJ3 between 17.6 and 14.5 ka, in good agreement in timing, duration and extent with the records from Hulu and Dongge caves and the Greenland ice core. The results indicate that there have been synchronous and significant climatic changes across monsoonal China and strong teleconnections between the North Atlantic and East Asia regions during the period 20-10 ka. This is much different from the Holocene Optimum which shows a time shift of more than several thousands years from southeast coastal to inland China. It is likely that temperature change at northern high latitudes during glacial periods exerts stronger influence on the Asian summer monsoon relative to insolation and appears to be capable of perturbing large-scale atmospheric/oceanic circulation patterns in the Northern Hemisphere and thus monsoonal rainfall and paleovegetation in East Asia. Climatic signals in the North Atlantic region propagate rapidly to East Asia during glacial periods by influencing the winter land-sea temperature contrast in the East Asian monsoon region.  相似文献   

First seismic record for intra-arc strike-slip tectonics along the Liquiñe-Ofqui fault zone at the obliquely convergent plate margin of the southern Andes     

D. Lange  J. Cembrano  A. Rietbrock  C. Haberland  T. Dahm  K. Bataille 《Tectonophysics》2008,455(1-4):14-24

A temporal seismic network recorded local seismicity along a 130 km long segment of the transpressional dextral strike-slip Liquiñe-Ofqui fault zone (LOFZ) in southern Chile. Seventy five shallow crustal events with magnitudes up to M_w 3.8 and depths shallower than 25 km were observed in an 11-month period mainly occurring in different clusters. Those clusters are spatially related to the LOFZ, to the volcanoes Chaitén, Michinmahuida and Corcovado, and to active faulting on secondary faults. Further activity along the LOFZ is indicated by individual events located in direct vicinity of the surface expression of the LOFZ. Focal mechanisms were calculated using deviatoric moment tensor inversion of body wave amplitude spectra which mostly yield strike-slip mechanisms indicating a NE–SW direction of the P-axis for the LOFZ at this latitude. The seismic activity reveals the present-day activity of the fault zone. The recent M_w 6.2 event near Puerto Aysén, Southern Chile at 45.4°S on April 21, 2007 shows that the LOFZ is also capable of producing large magnitude earthquakes and therefore imposing significant seismic hazard to this region.  相似文献   

Extensional Late Paleozoic deformation on the western margin of Pangea, Patlanoaya area, Acatlán Complex, southern Mexico     

M.A. Ramos-Arias  J.D. Keppie  A. Ortega-Rivera  J.W.K. Lee 《Tectonophysics》2008,448(1-4):60-76

New mapping in the northern part of the Paleozoic Acatlán Complex (Patlanoaya area) records several ductile shear zones and brittle faults with normal kinematics (previously thought to be thrusts). These movement zones separate a variety of units that pass structurally upwards from: (i) blueschist-eclogitic metamorphic rocks (Piaxtla Suite) and mylonitic megacrystic granites (Columpio del Diablo granite ≡ Ordovician granites elsewhere in the complex); (ii) a gently E-dipping, listric, normal shear zone with top to the east kinematic indicators that formed under upper greenschist to lower amphibolite conditions; (iii) the Middle–Late Ordovician Las Minas quartzite (upper greenschist facies psammites with minor interbedded pelites intruded by mafic dikes and a leucogranite dike from the Columpio del Diablo granite) unconformably overlain by the Otate meta-arenite (lower greenschist facies psammites and pelites): roughly temporal equivalents are the Middle–Late Ordovician Mal Paso and Ojo de Agua units (interbedded metasandstone and slate, and metapelite and mafic minor intrusions, respectively) — some of these units are intruded by the massive, 461 ± 2 Ma, Palo Liso megacrystic granite: decussate, contact metamorphic muscovite yielded a ⁴⁰Ar/³⁹Ar plateau age of 440 ± 4 Ma; (iv) a steeply-moderately, E-dipping normal fault; (v) latest Devonian–Middle Permian sedimentary rocks (Patlanoaya Group: here elevated from formation status). The upward decrease in metamorphic grade is paralleled by a decrease in the number of penetrative fabrics, which varies from (i) three in the Piaxtla Suite, through (ii) two in the Las Minas unit (E-trending sheath folds deformed by NE-trending, subhorizontal folds with top to the southeast asymmetry, both associated with a solution cleavage), (iii) one in the Otate, Mal Paso, and Ojo de Agua units (steeply SE-dipping, NE–SW plunging, open-close folds), to (iv) none in the Patlanoaya Group. ⁴⁰Ar/³⁹Ar analyses of muscovite from the earliest cleavage in the Las Minas unit yielded a plateau age of 347 ± 3 Ma and show low temperature ages of  260 Ma. Post-dating all of these structures and the Patlanoaya Group are NE-plunging, subvertical folds and kink bands. An E–W, vertical normal fault juxtaposes the low-grade rocks against the Anacahuite amphibolite that is cut by megacrystic granite sheets, both of which were deformed by two penetrative fabrics. Amphibole from this unit has yielded a ⁴⁰Ar/³⁹Ar plateau age of 299 ± 6 Ma, which records cooling through  490 °C and is probably related to a Permo-Carboniferous reheating event during exhumation. The extensional deformation is inferred to have started in the latest Devonian ( 360 Ma) during deposition of the basal Patlanoaya Group, lasting through the rapid exhumation of the Piaxtla Suite at  350–340 Ma synchronous with cleavage development in the Las Minas unit, deposition of the Patlanoaya Group with active fault-related exhumation suggested by Mississippian and Early Permian conglomerates ( 340 and 300 Ma, respectively), and continuing at least into the Middle Permian (≡ 260 Ma muscovite ages). The continuity of Mid-Continent Mississippian fauna from the USA to southern Mexico suggests that this extensional deformation occurred on the western margin of Pangea after closure of the Rheic Ocean.  相似文献   

Sedimentary petrology and geochemistry of siliciclastic rocks from the upper Jurassic Tordillo Formation (Neuquén Basin, western Argentina): Implications for provenance and tectonic setting     

Luis A. Spalletti  Ignasi Queralt  Sergio D. Matheos  Ferrn Colombo  Jorge Maggi 《Journal of South American Earth Sciences》2008,25(4):440-463

The Upper Jurassic Tordillo Formation is exposed along the western edge of the Neuquén Basin (west central Argentina) and consists of fluvial strata deposited under arid/semiarid conditions. The pebble composition of conglomerates, mineralogical composition of sandstones and pelitic rocks, and major- and trace-element geochemistry of sandstones, mudstones, and primary pyroclastic deposits are evaluated to determine the provenance and tectonic setting of the sedimentary basin. Conglomerates and sandstones derived almost exclusively from volcanic sources. The stratigraphic sections to the south show a clast population of conglomerates dominated by silicic volcanic fragments and a predominance of feldspathic litharenites. This framework composition records erosion of Triassic–Jurassic synrift volcaniclastic rocks and basement rocks from the Huincul arch, which was exhumed as a result of Late Jurassic inversion. In the northwestern part of the study area, conglomerates show a large proportion of mafic and acidic volcanic rock fragments, and sandstones are characterised by a high content of mafic volcanic rock fragments and plagioclase. These data suggest that the source of the sandstones and conglomerates was primarily the Andean magmatic arc, located west of the Neuquén Basin. The clay mineral assemblage is interpreted as the result of a complex set of factors, including source rock, climate, transport, and diagenesis. Postdepositional processes produced significant variations in the original compositions, especially the fine-grained deposits. The Tordillo sediments are characterised by moderate SiO₂ contents, variable abundances of K₂O and Na₂O, and a relatively high proportion of ferromagnesian elements. The degree of chemical weathering in the source area, expressed as the chemical index of alteration, is low to moderate. The major element geochemistry and Th/Sc, K/Rb, Co/Th, La/Sc, and Cr/Th values point to a significant input of detrital volcanic material of calcalkaline felsic and intermediate composition. However, major element geochemistry is not useful for interpreting the tectonic setting. Discrimination plots based on immobile trace elements, such as Ti, Zr, La, Sc, and Th, show that most data lie in the active continental margin field. Geochemical information is not sufficiently sensitive to differentiate the two different source areas recognized by petrographic and modal analyses of conglomerates and sandstones.  相似文献   

First U–Pb SHRIMP age of the Hauterivian stage, Neuquén Basin, Argentina     

M. Beatriz Aguirre-Urreta  Pablo J. Pazos  Darío G. Lazo  C. Mark Fanning  Vanesa D. Litvak   《Journal of South American Earth Sciences》2008,26(1):91-99

A high-resolution ion-microprobe (SHRIMP) U–Pb zircon age from a tuff layer intercalated in the ammonoid bearing sedimentary succession of the Neuquén Basin in Argentina provides a robust geochronologic date to add to the absolute ages and to improve the relative chronology of the Early Cretaceous Hauterivian stage. The tuff layer appears interbedded between shales of the upper member (Agua de la Mula) of the Agrio Formation within the Spitidiscus riccardii ammonoid zone (base of the Late Hauterivian) yielding a date of 132.5 ± 1.3 Ma. This date confirms and supports an accurate correlation between the ammonoid biostratigraphy of the Neuquén Basin with the Western Mediterranean Province of the Tethys during the Early Cretaceous and matches with the most recently published time scale. It also casts doubts on the validity of K–Ar ages on glauconite-grains recently reported from the Lower Cretaceous of the Vocontian Basin of France.  相似文献   

淡水双壳类壳体碳同位素研究:以河蚬(corbicula fluminea,Müller 1774)为例   总被引：2，自引：0，他引：2  

闫慧  李心清  周会 《地球化学》2008,37(3)

双壳类壳体碳酸盐(文石)稳定同位素组成已被广泛地用于古气候和古环境重建研究中,但是双壳类壳体碳同位素组成所指示的气候和环境意义一直是争议的问题.对双壳类河蚬(corbicula fluminea)进行了室内养殖,并选取两个壳体样品(壳高,A=13 mm,B=9mm),测定其生长部分壳体和生长期间水体碳同位素,研究表明,随着水体碳同位素的升高(δ13CDIC由-5.24‰升至1.41‰),两壳体碳同位素也随之升高,表明水体对壳体碳同位素的影响;δ13CA分布范围为-4.76‰～2.09‰,δ13CB为-8.49‰～2.89,壳体A和B碳同位素均比预测平衡值偏负,表明壳体在形成过程中利用了新陈代谢产生的富集12C的CO2.根据计算壳体A在实验中沉淀部分壳体利用新陈代谢碳的比例(M值)为24%～43%,平均值为33%;壳体B为33%～75%,平均值为58%.M值随生物的生长呈下降变化,这说明在实验中河蚬主要是通过增加对DIC的吸收和利用来满足壳体生长对物质量增加的需求.  相似文献   

三肇凹陷青山口组源岩生成油向下“倒灌”运移层位及其研究意义   总被引：14，自引：1，他引：13  

付广  王有功 《沉积学报》2008,26(2):355-360

为了研究三肇凹陷青山口组源岩生成的油向下“倒灌”运移层位,对油向下“倒灌”运移机制及条件进行了研究,得到三肇凹陷扶杨油层同时具备①青山口组源岩目前应具有足够大的超压;②存在连通青山口组源岩和扶杨油层的T2断裂2个条件,青山口组源岩生成的油能够在超压的作用下在嫩江组沉积末期、明水组沉积末期和古近系沉积末期通过T2断裂向下伏扶杨油层中“倒灌”运移。利用压力封闭原理,对三肇凹陷青山口组源岩生成的油向下“倒灌”运移距离进行了研究,得到三肇凹陷青山口组源岩生成的油向下“倒灌”运移距离一般大于500 m,而三肇凹陷扶杨油层地层厚度最大只有500 m,表明三肇凹陷青山口组源岩生成的油可以向下“倒灌”运移至整个扶杨油层的任何部位。目前三肇凹陷扶杨油层从上至下均含油,且已找到的油藏均分布于青山口组源岩生成的油能够向下“倒灌”运移分布范围内或附近,这表明青山口组源岩生成的油向下“倒灌”运移层位控制着油气富集层位,青山口组源岩生成的油向下“倒灌”运移分布范围控制着三肇凹陷扶杨油层油藏形成与分布范围。青山口组源岩生成的油向下“倒灌”运移分布范围及其附近应是三肇凹陷扶杨油层油下一步勘探的有利地区。  相似文献