Capture orbits and melnikov integrals in the planar three-body problem

The separatrix between bounded and unbounded orbits in the three-body problem is formed by the manifolds of forward and backward parabolic orbits. In an ideal problem these manifolds coincide and form the boundary between the sets of bounded and unbounded orbits. As a mass parameter increases the movement of the parabolic manifolds is approximated numerically and by Melnikov's method. The evidence indicates that for positive values of the mass parameter these manifolds no longer coincide, and that capture and oscillatory orbits exist.     

Equilibrium solutions of the restricted problem of 2 + 2 axisymmetric rigid bodies

The restricted problem of 2 + 2 homogenous axisymmetric ellipsoids such that their equatorial planes coincide with the orbital plane of the centers of mass is considered. The equilibrium solutions of this problem are shown to exist. Six of these solutions are located about the collinear points of the restricted problem of three axisymmetric ellipsoids. A special case of this problem is studied and sixteen solutions are found in the neighborhood of the triangular Lagrangian points.     

On the Sitnikov problem

A mapping which reflects the properties of the Sitnikov problem is derived. We study the mapping instead of the original differential equations and discover that there exists a hyperbolic invariant set. The theoretical prediction of the disorder region agrees remarkably with numerical results. We also discuss the LCEs and KS-entropy of the dynamical system.This project is supported by the National Science Foundation of China.     

Central configurations of the planar 1+N body problem

In this paper, we give a new derivation of the equations for the central configurations of the 1+n body problem. In the case of equal masses, we show that forn large enough there exists only one solution. Our lower bound forn improves by several orders of magnitude the one previously found by Hall.     

A local identification technique for geotechnical and geophysical systems

Geotechnical structures and natural soil deposits are massive multi‐phase particulate systems characterized by the development of localized response mechanisms under extreme loading conditions. Identification and analysis of such systems based on inverse boundary value problem formulations and sparse measurements are generally indeterminate. This paper presents an alternative local inverse problem technique. Point‐wise identification analyses of the constitutive behaviour of water‐saturated geotechnical and geophysical systems are performed using acceleration and pore pressure records provided by a cluster of closely spaced sensors. The developed novel technique does not require the availability of boundary condition measurements, or solution of an associated boundary value problem. The constitutive behaviour at a specific location of a soil‐system is analysed independently of adjacent response mechanisms or material properties. Numerical simulations and centrifuge tests of a soil‐retaining wall system are used to demonstrate the capabilities of the developed technique. Copyright © 2003 John Wiley & Sons, Ltd.     

Investigation of the long-periodic orbits of Trojan-type asteroids in the outer solar system

The present paper demonstrates the results of the numerical integration of equations of motion of a infinitesimal mass pleased in the neighborhood of the triangular point of the Sun-planet system. There are presented the results for the outer solar system, i.e. for Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. The long-periodic solutions were searched for the distance from the Lagrangian point changing from ±0.01 to ±0.10 in canonical units. The Trojans of those planets have the circle, tadpole, horseshoe and irregular shape of their orbits. Same of those test particles showed a close approach to planet. Other of those collided with planet and then was removed from the solar system. The tadpole, circle and same trajectories surveyed integration for 100,000 years. This revised version was published online in July 2006 with corrections to the Cover Date.     

孔隙砂岩力学性质随埋深变化的三轴试验研究

针对取自吐-哈盆地中侏罗统油储地层砂岩(J_(2s))进行了三轴压缩试验,设计了不同的温度、压力及含水组台条件来模拟地层埋深对岩石力学性质的影响.初步结果表明,J_(2s)砂岩的主要静态岩石力学参数(杨氏模量、抗压强度、抗剪强度、弹性极限应力.残余强度及最大轴向承载应变量等)都呈明显的“组合”变化.随着埋深增大(0-5000m),杨氏模量总体呈下降趋势,其余各量皆有不同程度的增加,还对温压组合条件下砂岩断面上的摩擦滑动性能进行了分析讨论.结果对油储工程稳定性研究及油储地层地球物理反演时地层弹性参数的选取皆具有一定的参考意义.     

Certain Comments on V. Szebehely's Paper 'Open Problems on the Eve of the Next Millennium'

An equation for inverse problem considerations, offered by V. Szebehely in the above paper, is amended and its applicability is discussed.     

一类非线性二阶奇异初值问题的正解

在简单的假定下。建立了一类非线性二阶奇异初值问题C^1[0,1]正解存在的充分必要条件，我们的奇异问题在有奇性。     

Critical symmetric periodic orbits in the photogravitational restricted three-body problem

In this paper, we determine series of horizontally critical symmetric periodic orbits of the six basic families, f,g,h,i,l,m, of the photogravitational restricted three-body problem, and computetheir vertical stability. We restrict our study in the case where only the first primary is radiating, namely q ₁≠1 andq ₂=1. We also compare our results with those of Hénon and Guyot (1970) so as to study the effect of radiation to this kind of orbits. This revised version was published online in July 2006 with corrections to the Cover Date.