含有集约束向量极值问题的最优性条件

在序线性拓扑空间里研究了含有集约束向量极值问题的最优性条件,并建立了充分性和必要性条件.     

Frequency analysis of a dynamical system

Frequency analysis is a new method for analyzing the stability of orbits in a conservative dynamical system. It was first devised in order to study the stability of the solar system (Laskar, Icarus, 88, 1990). It is a powerful method for analyzing weakly chaotic motion in hamiltonian systems or symplectic maps. For regular motions, it yields an analytical representation of the solutions. In cases of 2 degrees of freedom system with monotonous torsion, precise numerical criterions for the destruction of KAM tori can be found. For a 4D symplectic map, plotting the frequency map in the frequency plane provides a clear representation of the global dynamics and describes the actual Arnold web of the system.     

DCMT光电扫描主测微器的设计与研究

DCMT主测微器不同于其它类型的子午环测微器,它具有自校准测定仪器参数的功能。该测微器采用了活动光栅的方案,其优点是能观测近极星和各类准直像;活动光栅另一个显著优点是不同赤纬星几乎可用相同的观测时间.对“V”形光栅的工作原理和误差进行了详细讨论,并给出了一组严格的公式。其系统误差来源有:光栅形状改正、光栅驱动方向相对于光栅的倾斜、光栅驱动方向相对于赤径方向的倾斜、星径曲率改正。     

Geometric Derivation of the Delaunay Variables and Geometric Phases

We derive the classical Delaunay variables by finding a suitable symmetry action of the three torus T³ on the phase space of the Kepler problem, computing its associated momentum map and using the geometry associated with this structure. A central feature in this derivation is the identification of the mean anomaly as the angle variable for a symplectic S ¹ action on the union of the non-degenerate elliptic Kepler orbits. This approach is geometrically more natural than traditional ones such as directly solving Hamilton–Jacobi equations, or employing the Lagrange bracket. As an application of the new derivation, we give a singularity free treatment of the averaged J ₂-dynamics (the effect of the bulge of the Earth) in the Cartesian coordinates by making use of the fact that the averaged J ₂-Hamiltonian is a collective Hamiltonian of the T³ momentum map. We also use this geometric structure to identify the drifts in satellite orbits due to the J ₂ effect as geometric phases.     

Numerical Stabilization of Orbital Motion

Mainly, the author focuses on Baumgarte's method and its applications in satellite, asteroid, stellar and planetary problems. In the paper arguments are given for the use of energy relations for stabilization in the elliptical two-body problem. Stabilizing properties of Baumgarte's equations and others are discussed. A simple approach is proposed for stabilizing the equations of almost circular motion. By using Baumgarte's technique, the author derives stabilized equations of perturbed restricted three-body problem. It is shown experimentally that stabilization in the problems mentioned above can raise the accuracy of numerical integration by several orders.     

疏散星团NGC6530天区的恒星自行和成员概率

利用上海天文台的照相底片资料,确定了疏散星团NGC6530天区364颗恒星的自行和成员概率,并对有关自行测定的方法、结果和精度等问题作了较为详细的介绍和讨论。使用的底片历元差为87年,全部恒星自行中误差的均方根值为1．09mas/a。     

华南前寒武系基底变质杂岩和中-新生代地幔岩的稀有气体同位素组成及其大地构造意义

对华南前寒武系变质岩浆杂岩稀有气体He、Ne、Ar和Xe的系统研究表明:扬子克拉通基底为含高³He的下地壳"原始岩石层",(³He/⁴He)×10^-6比值为2.8～4.6;而华夏板块基底变质岩浆杂岩则是在缺乏³He、低(³He/⁴He)×10^-8比值(3.15～17.7)的构造环境下形成的大陆中-上地壳变质岩浆杂岩层,反映出两者基底性质迥然不同。华南中-新生代爆破岩筒He同位素组成相反,相对稳定的扬子克拉通(³He/⁴He)×10^-8比值仅0.18～4.22,而郯庐-四会-吴川断裂以东,中-新生代活动地块(太平洋构造域)(³He/⁴He)×10^-8比值高达3.7～20.5。He同位素表明郯庐-四会-吴川断裂带为切割深至地幔的边界深大断裂,是扬子克拉通与华夏板块间的边界且控制了燕山期火山-侵入岩浆向西扩展。Ar同位素组成表明华南大陆中-新生代地幔形成接近"均一"的地幔组份。¹³⁶Xe/¹³⁰Xe-¹²⁹Xe/¹³⁰Xe相关组份表明它们具有地幔柱岩石同位素组成特征。     

Ground motion estimation during the Kashmir earthquake of 8th October 2005

In this article, analytical methods have been used to estimate ground motion during the 8 October 2005, Kashmir earthquake. Peak ground acceleration (PGA) values at several stations in the epicentral region have been estimated by empirical analytical source mechanism models. As an alternate analysis, PGA estimates have also been obtained using the stochastic finite fault seismological model. The estimated PGAs are compared with that obtained from damage values. A PGA contour map in the near-source region is provided. It is found that very near to the epicenter, PGA would have reached more than 1 g. It is demonstrated that empirical analytical models can be effectively used to estimate ground motion due to rupture of active faults.