Perturbed Robe’s circular restricted three-body problem under an Oblate Primary

This paper examines the existence and linear stability of equilibrium points in the perturbed Robe’s circular restricted three-body problem under the assumption that the hydrostatic equilibrium figure of the first primary is an oblate spheroid. The problem is perturbed in the sense that small perturbations are given to the Coriolis and centrifugal forces are being considered. Results of the analysis found two axial equilibrium points on the line joining the centre of both primaries. It is further observed that under certain conditions, points on the circle within the first primary are also equilibrium points. And a special case where the density of the fluid and that of the infinitesimal mass are equal (D = 0) is discussed. The linear stability of this configuration is examined; it is observed that the first axial point is unstable while the second one is conditionally stable and the circular points are unstable.     

太阳多方模型对行星轨道要素变化的长期摄动影响

本文利用天体力学中的摄动理论和天体物理学中的气体星多方模型理论研究了太阳多方模型对行星轨道要素变化的长期摄动影响。文中给出了太阳日多方指数ｎ＝３的模型由于自转、扁度和内部密度分布等因素对行星轨道要素变化的长期摄动效应的理论结果。研究结果表明：行星轨道要素除长轴、偏心率和轨道倾角不受长期摄动外升交点经度、近日点经度以及平近点角均受长期摄动的影响。最后利用理论结果对行星轨道要素的长期投动效应做了数值计算，数值结果在表１中给出。     

Direct Calculation Methods of Hansen Coefficients and Their Derivatives

Seven direct calculation methods of Hansen coefficients and their derivatives are reviewed. The computational efficiencies of these methods are compared, and their computational stabilities are analyzed. We show that the recursion relations of Hansen coefficients can be used to determine the stabilities of calculation results. Finally, it is pointed out that Wnuk's method (double precision computation) and McClain's methods (quadruple precision computation) are stable, which can be used to calculate orbit perturbations. Because of small orbital eccentricities of most satellites, the perturbation calculations without singularities are required, and McClain's first method (quadruple precision computation) is recommended.     

地球横向不均匀结构对地表以及空间固定点同震重力变化的影响

本文提出一个新算法,用来高精度计算三维不均匀地球模型中地震位错引起的地表以及空间固定点同震重力变化.具体地说,我们首先把实际三维不均匀地球分解成球对称地球模型和对应的横向不均匀增量,分别进行计算,二者对应的计算结果分别称为球对称解和三维响应.由于球对称解可直接利用球对称地球模型位错理论计算得到,本文的目标是计算三维响应即地球的横向不均匀结构对同震重力变化的影响.然后,我们把三维响应再分为震源的响应和地球横向不均匀结构的响应,它们可分别借助对震源函数的扰动以及对平衡方程式的变分求解.本文推导出六个特殊点源位错引起的地表以及空间固定点同震重力变化计算公式(一个垂直走滑位错,两个相互垂直的倾滑位错,三个开裂位错),对这些公式进行适当组合就可以计算任意位置任意类型位错产生的同震重力变化,对应的计算公式同步给出.接着,依据36阶P波速度模型,我们利用岩石试验经验关系式推导出三维S波速度模型,密度模型,位场模型以及重力模型.最后,利用上述三维模型,本文计算出三种典型类型的点源位错产生的同震重力变化,结果显示三维响应与位错类型,震源深度都有关系,其最大响应占球对称解的0.5%左右,且在所有影响因素中S波速度模型影响最大.数值结果同时表明,三维响应中震源的响应与地球横向不均匀构造的响应处于同一量级.本文给出的地表和空间固定点同震重力变化计算公式可分别高精度解析地表重力和卫星重力观测数据(GRACE、GOCE等),提高大地测量数据理论解析水平.     

夏季逐月东亚高空急流异常对我国降水的影响

根据1981～2010年NCEP/DOE再分析资料与中国160站降水资料,利用统计学、物理量诊断等方法,探讨夏季东亚季风环流系统重要成员——东亚高空西风急流位置、强度逐月变化与我国降水的关系。分析表明:6～8月东亚高空西风急流比各自气候态位置偏南(北)时,易造成6月华南、江南地区降水、7月江淮流域降水以及8月长江中上游地区降水偏多(少)。本文重点分析2010年6月、2007年7月及2006年8月东亚高空西风急流位置异常时东亚高、低纬度环流特征及其对我国降水影响的物理成因。研究发现:2010年6月东亚高空西风急流稳定在35°N以南。急流轴南侧(北侧)为强辐散(辐合)距平,相应低层辐合(辐散),造成江南、华南地区从低层至高层的强上升运动,配合整层偏西水汽通量距平,为该地区持续性降水提供了有利的动力和水汽条件;2007年7月东亚高空急流位置偏南、强度偏弱,急流月内尺度扰动偏强,使得东亚中高纬度冷空气活动频繁,造成淮河流域出现持续性暴雨;2006年8月东亚高空西风急流位置持续偏北、强度偏强,有利西太平洋副高西伸、北抬,我国四川—重庆地区受副高控制,出现了极端高温干旱天气。     

层状介质二维电阻率扰动反演方法

为解决考古、工程地质和地下水污染勘查中某些探测靶体与周围介质间电性差异不大的地质问题,本文提出了层状介质背景下二维电阻率扰动反演方法．根据观测得到的背景剖面视电阻率断面,确定出背景场的电性层结构,利用电阻率扰动方法计算出敏感矩阵,通过广义逆矩阵法求解出电阻率的增量．在商丘地下夯土城墙的应用表明,该方法有效地抑制了夯土城墙的旁侧效应和地下水噪声的影响,揭示出地下夯土城墙的埋深与几何形态．     

在非比例阻尼情况下结构动力响应的摄动分析方法

本文将摄动方法应用于非比例阻尼系统，将一个非比例阻尼问题转化为一系列比例阻尼问题叠加的形式，从数学上对结构运动方程进行了较严格的求解，给出了在简谐荷载情况下的响应计算公式，并对所给方法的收敛性进行了研究，给出了相应的收敛条件。文中通过算例证明了本文方法的正确性与有效性。     

Scattering of internal waves in a two-layer fluid flowing through a channel with small undulations

Using two-dimensional linear water wave theory, we consider the problem of normal water wave (internal wave) propagation over small undulations in a channel flow consisting of a two-layer fluid in which the upper layer is bounded by a fixed wall, an approximation to the free surface, and the lower one is bounded by a bottom surface that has small undulations. The effects of surface tension at the surface of separation is neglected. Assuming irrotational motion, a perturbation analysis is employed to calculate the first-order corrections to the velocity potentials in the two-layer fluid by using Green’s integral theorem in a suitable manner and the reflection and transmission coefficients in terms of integrals involving the shape function c(x) representing the bottom undulation. Two special forms of the shape function are considered for which explicit expressions for reflection and transmission coefficients are evaluated. For the specific case of a patch of sinusoidal ripples having the same wave number throughout, the reflection coefficient up to the first order is an oscillatory function in the quotient of twice the interface wave number and the ripple wave number. When this quotient approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of the incident wave energy occurs if this number is large. Again, when a patch of sinusoidal ripples having two different wave numbers for two consecutive stretches is considered, the interaction between the bed and the interface near resonance attains in the neighborhood of two (singular) points along the x-axis (when the ripple wave number of the bottom undulation become approximately twice as large as the interface wave number). The theoretical observations are presented in graphical form.     

Numerical and experimental studies of a floating and liquid-filled membrane structure in waves

Linear theories to analyse a floating and liquid-filled membrane structure in head- and beam-sea waves have been presented. The dynamic solutions are based on a small perturbation of the static solution, and the hydroelastic deformation has been taken care of correctly to the first order of the incident wave amplitude. A new experiment has been carried out for measuring the dynamic tensions of a membrane. A comparison between the theories and experiment are presented for the dynamic hoop tension.