Stable Manifolds and Homoclinic Points Near Resonances in the Restricted Three-Body Problem

The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses 1− μ and μ that circle each other with period equal to 2π. For small μ, a resonant periodic motion of the massless particle in the rotating frame can be described by relatively prime integers p and q, if its period around the heavier primary is approximately 2π p/q, and by its approximate eccentricity e. We give a method for the formal development of the stable and unstable manifolds associated with these resonant motions. We prove the validity of this formal development and the existence of homoclinic points in the resonant region. In the study of the Kirkwood gaps in the asteroid belt, the separatrices of the averaged equations of the restricted three-body problem are commonly used to derive analytical approximations to the boundaries of the resonances. We use the unaveraged equations to find values of asteroid eccentricity below which these approximations will not hold for the Kirkwood gaps with q/p equal to 2/1, 7/3, 5/2, 3/1, and 4/1. Another application is to the existence of asymmetric librations in the exterior resonances. We give values of asteroid eccentricity below which asymmetric librations will not exist for the 1/7, 1/6, 1/5, 1/4, 1/3, and 1/2 resonances for any μ however small. But if the eccentricity exceeds these thresholds, asymmetric librations will exist for μ small enough in the unaveraged restricted three-body problem.     

Isograds and P–T evolution in the eastern Lepontine Alps (Graubünden, Switzerland)

Reactions producing Al‐rich index minerals in the south‐eastern part of the Lepontine Dome (Central Alps, Switzerland) are investigated using mineral distribution maps, microstructural observations and equilibrium phase diagrams. The apparent staurolite mineral zone boundary corresponds to the paragonite breakdown reaction Pg + Grt + Qtz = Pl + Al₂O₃ + W. Equilibrium phase diagrams show that most natural metapelites do not contain staurolite or alumosilicates as long as univalent cations are predominantly accommodated in white mica. For a wide range of metapelitic compositions the paragonite breakdown releases sufficient Al for the formation of these minerals. Rare occurrences of staurolite and kyanite, north of the formerly mapped mineral zone boundaries, coexist with paragonite and are restricted to extremely Al‐rich bulk compositions. The stable branch of the kyanite‐forming paragonite breakdown reaction above 660 °C yields an additional mapable isograd. The second set of Al‐releasing reactions is biotite‐producing phengite breakdown. However, these reactions are less suitable to produce well defined reaction isograds in the field as they are more continuous and their progress is strongly dependent on bulk composition. Well developed fibrolite in metapelites does not appear until staurolite starts to breakdown. We conclude that amphibolite facies conditions in the study area were attained by decompression, without substantial heating at low pressures.     

Novel Analysis of Tadpole and Horseshoe Orbits

A simple analysis of tadpole and horseshoe orbits is performed using a new perturbation technique. The first-order results are presented explicitely, extension to any perturbation order is delineated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Paleo-glacial reconstruction of the Thajwas glacier in the Kashmir Himalaya using 10Be cosmogenic radionuclide dating

Quantitative glacial chronologies of past glaciations are sparse in the Himalaya, and mostly absent in the Kashmir Himalaya. We used cosmogenic ¹⁰Be exposure dating, and geomorphological mapping to reconstruct glacial advances of the Thajwas Glacier (TG) in the Great Himalayan Range of the Kashmir Himalaya. From ¹⁰Be exposure dating of ten moraine boulders, four glacial stages with ages ～20.77 ± 2.28 ka, ～11.46 ± 1.69 ka, ～9.12 ± 1.39 ka and ～4.19 ± 0.78 ka, were identified. The reconstructed cosmogenic radionuclide ages confirmed the global Last Glacial Maximum (gLGM), Younger Dryas, Early Holocene, and Neoglaciation episodes. As per area and volume change analyses, the TG has lost 51.1 km² of its area and a volume of 2.64 km³ during the last 20.77 ± 2.28 ka. Overall, the results suggested that the TG has lost 64% of area and 73% of volume from the Last glacial maximum to Neoglaciation and about 85.74% and 87.67% of area and volume, respectively, from Neoglaciation to the present day. The equilibrium line altitude of the TG fluctuated from 4238 m a.s.l present to 3365 m a.s.l during the gLGM (20.77 ± 2.28 ka). The significant cooling induced by a drop in mean ambient temperature resulted in a positive mass balance of the TG during the gLGM. Subsequently the melting accelerated due to the continuing rise of the global ambient temperature. Paleo-glacial history reconstruction of the Kashmir Himalaya, with its specific geomorphic and climatic setting, would help close the information gap about the chronology of past regional glacial episodes.     

顾及时空特性的SBAS高质量点选取算法

SBAS技术中常用的相干系数选点方法受旁瓣效应的影响,容易造成部分高质量点的漏选以及低质量点的误选。针对这一问题,本文提出了顾及时空特性的SBAS高质量点选取算法,根据干涉相位各个成分的空间特性,分离出噪声相位判别点的质量。试验表明考虑同质点的Non-Local滤波能够更加可靠地提取干涉相位中的空间相关相位,从而提高噪声相位估计的准确性。利用覆盖上海地区1992—1998年的24景JERS-1影像作为试验数据,分别用相干系数法以及本文的方法进行选点。结果表明本文算法能够有效地选出相干系数法在农田与村落交错地区漏选的高质量点,同时排除了相干系数法由于旁瓣效应影响的误选点。     

比例射线移位算法的改进及其应用

点状要素群移位的比例射线算法能够较好地保持移位后点群的空间分布模式。文中从农村居民地群移位的实际要求出发,对比例射线移位算法进行了改进:首先考虑居民地面积的不同大小对移位的影响;其次,设计比例射线移位的迭代方法;最后对于非常邻近的居民地群的移位,采用"微小"移位方法。通过实验验所改进的算法是有效的。     

三维激光扫描测量精度评定的讨论

三维激光扫描点转换到工程测量坐标系时,误差来源多、类型多,目前尚没有一套完整的精度评定方法体系。本文对误差源进行分析,将其误差归纳为标准控制点测量误差、扫描误差和坐标转换模型误差三大类;探讨了扫描点在工程测量坐标系中的位置误差指标体系,给出了体系中各项精度指标的计算方法,为三维激光扫描测量在不同的应用中提供一套系统的精度评定参考。     

采用Morse理论的小尺度地形特征提取方法

Li DAR点云为小尺度地表形态的提取与表达提供了精确的数据源,但其高密度性与不确定性,导致应用Morse理论提取的特征点中含有大量的"伪特征点"。这里首先通过定义特征点指数等一系列概念,模拟特征点周围区域的地表形态,建立特征点重要性度量指标与计算方法;然后给出了地表重要特征点的提取算法;最后,进行了试验验证与分析。结果表明:提出的算法优于现有的持续值法与自然法则法,可以有效剔除"伪特征点",实现基于Li DAR点云小尺度复杂地形的特征点精确提取与多层次表达。     

基于区域多次回波点密度分析的城区LiDAR建筑物提取

以正确提取城区Li DAR点云中建筑物为目标,综合利用不同类别目标点云的回波特征以及地形信息,提出了一种基于区域多次回波密度分析的Li DAR点云建筑物提取方法。首先,将点云构建不规则三角网(triangulated irregular network,TIN),获取封闭的等高线;然后,利用等高线间的拓扑关系得到等高线族区域;最后,统计每一区域的多次回波点云密度信息,通过建筑物和树木区域多次回波点云在区域密度上的巨大差异来识别建筑物点云和树木点云。研究结果表明:该方法既充分利用了建筑物表面与植被间多次回波特性的差异,又不否定建筑物边缘同样存在多次回波的现象;通过封闭的等高线自适应地检测出地物目标的轮廓,弥补了传统Li DAR建筑物提取方法的不足;该方法能够较其他方法更准确地提取建筑物。     

Lambert problem solution in the hill model of motion

The goal of this paper is obtaining a solution of the Lambert problem in the restricted three-body problem described by the Hill equations. This solution is based on the use of pre determinate reference orbits of different types giving the first guess and defining the sought-for transfer type. A mathematical procedure giving the Lambert problem solution is described. This procedure provides step-by-step transformation of the reference orbit to the sought-for transfer orbit. Numerical examples of the procedure application to the transfers in the Sun–Earth system are considered. These examples include transfer between two specified positions in a given time, a periodic orbit design, a halo orbit design, halo-to-halo transfers, LEO-to-halo transfer, analysis of a family of the halo-to-halo transfer orbits. The proposed method of the Lambert problem solution can be used for the two-point boundary value problem solution in any model of motion if a set of typical reference orbits can be found.