Homoclinic and heteroclinic orbits in the photogravitational restricted three-body problem

We study numerically the asymptotic homoclinic and heteroclinic orbits around the hyperbolic Lyapunov periodic orbits which emanate from Euler's critical points L ₁ and L ₂, in the photogravitational restricted plane circular three-body problem. The invariant stable-unstable manifolds associated to these Lyapunov orbits, are also presented. Poincaré surface of sections of these manifolds on appropriate planes and several homoclinic and heteroclinic orbits for the gravitational case as well as for varying radiation factor q ₁, are displayed. Homoclinic-homoclinic and homoclinic-heteroclinic-homoclinic chains which link the interior with the exterior Hill's regions, are illustrated. We adopt the Sun-Jupiter system and assume that only the larger primary radiates. It is found that for small deviations of its value from the gravitational case (q ₁ = 1), the radiation pressure exerts a significant impact on the Hill's regions and on these asymptotic orbits.     

An implementation ofN-body chain regularization

The chain regularization method (Mikkola and Aarseth 1990) for high accuracy computation of particle motions in smallN-body systems has been reformulated. We discuss the transformation formulae, equations of motion and selection of a chain of interparticle vectors such that the critical interactions requiring regularization are included in the chain. The Kustaanheimo-Stiefel (KS) coordinate transformation and a time transformation is used to regularize the dominant terms of the equations of motion. The method has been implemented for an arbitrary number of bodies, with the option of external perturbations. This formulation has been succesfully tested in a generalN-body program for strongly interacting subsystems. An easy to use computer program, written inFortran, is available on request.     

大瑞铁路高黎贡山越岭段主要工程地质问题与地质选线

在野外地质调查、钻探、地应力测量和室内测试分析的基础上,对大瑞铁路高黎贡山越岭段规划设计中可能遇到的高地温、高地应力、活动断裂断错、岩爆、涌水突泥、软岩大变形和边坡稳定性等主要工程地质问题进行了论述,认为高地温和热害是制约高黎贡山深埋隧道段建设的关键因素。根据地热钻探、测试资料分析,该区的地热分布受断裂构造控制明显,黄草坝断裂具有阻水隔热的工程地质特性。对比分析认为,C12K方案(34.5 km越岭长隧道方案)位于黄草坝阻水隔热断层之南,通道内相对低温,且在隧道口处避让了古滑坡等不利工程地质问题,在众多比选方案中工程地质条件较好。调查研究结果对大瑞铁路全线贯通具有重要意义。     

地理国情普查基本统计实践与经验探讨

基于地理国情普查基本统计软件,利用地理国情普查数据,开展了基本统计试验,通过试验出现的问题,总结了基本统计工作中需要注意的事项包括统计分析前数据检查、数据预处理、坡度带分层及融合和成果质量检查等,避免出现统计错误,并提出了基本统计成果应与其他行业专题资料进行对比分析的建议,为地理国情普查基本统计工作提供了参考。     

Reducing background effects in orchards through spectral vegetation index correction

Satellite remote sensing provides an alternative to time-consuming and labor intensive in situ measurements of biophysical variables in agricultural crops required for precision agriculture applications. In orchards, however, the spatial resolution causes mixtures of canopies and background (i.e. soil, grass and shadow), hampering the estimation of these biophysical variables. Furthermore, variable background mixtures obstruct meaningful comparisons between different orchard blocks, rows or within each row. Current correction methodologies use spectral differences between canopies and background, but struggle with a vegetated orchard floor. This background influence and the lack of a generic solution are addressed in this study.Firstly, the problem was demonstrated in a controlled environment for vegetation indices sensitive to chlorophyll content, water content and leaf area index. Afterwards, traditional background correction methods (i.e. soil-adjusted vegetation indices and signal unmixing) were compared to the proposed vegetation index correction. This correction was based on the mixing degree of each pixel (i.e. tree cover fraction) to rescale the vegetation indices accordingly and was applied to synthetic and WorldView-2 satellite imagery. Through the correction, the effect of background admixture for vegetation indices was reduced, and the estimation of biophysical variables was improved (ΔR² = 0.2–0.31).     

台风麦莎登陆后粘性摩擦对正压特征波动的影响

本文推导出柱坐标系下含有粘性摩擦项的正压方程组。选取2005年台风麦莎登陆浙江过程中的8月6日15时的WRF(Weather Research and Forecasting)模式输出资料,利用数值差分方法对该正压方程组求特征波解,分析粘性摩擦对台风麦莎内部正压特征波动的影响。结果表明,重力惯性外波在粘性摩擦的影响下,最不稳定波的波数为45左右,波动在摩擦的影响下衰减,波动沿逆时针传播,在半径1000 km处,1波波速为47.43 m/s,在半径r>800 km的范围内,径向风分量扰动加大,辐合辐散运动增强;而摩擦影响下的涡旋Rossby波,2波最不稳定,波动增长率减小,在半径r=200 km处波动相速度为4.282~29.172 m/s,扰动涡度大值区范围减小,涡旋Rossby波的波动区域沿着径向向台风中心收缩。分析包含所有波动时,考虑摩擦后,最不稳定波数在45左右且波动衰减,1波波速在r=1000 km处(外螺旋雨带)为26.374 m/s;在半径r=200 km(内螺旋雨带)为5.275 m/s,考虑径向基本气流后,最不稳定波的波数保持不变,半径r=1000 km处的波速增加为30.324 m/s,r=200 km(内螺旋雨带)处波速为6.065 m/s,摩擦使得径向风分量扰动明显增大,辐合辐散运动加强。     

Numerical Determination of Homoclinic and Heteroclinic Orbits at Collinear Equilibria in the Restricted Three-Body Problem with Oblateness

Asymptotic motion to collinear equilibrium points of the restricted three-body problem with oblateness is considered. In particular, homoclinic and heteroclinic solutions to these points are computed. These solutions depart asymptotically from an equilibrium point and arrive asymptotically at the same or another equilibrium point and are important reference solutions. To compute an asymptotic orbit, we use a fourth order local analysis, numerical integration and standard differential corrections.     

Libration Points in Schwarzschild's Circular Restricted Three-Body Problem

The restricted three-body problem in Schwarzschild's gravitational field is analyzed. The existen- ce of the equilibrium points in the orbital plane is discussed and the corresponding positions are established. There are three collinear libration points, and, if they exist, two triangular libration points (situated in the orbital plane of the primaries). If triangular points exist, they may not form equilateral triangles; the triangles are isosceles for equal masses of the primaries, and scalene else.     

On the variational approach to the periodic n-body problem

This expository paper gathers some of the results obtained by the author in recent works in collaboration with Davide Ferrario and Vivina Barutello, focusing on the periodic n-body problem from the perspective of the calculus of variations and minimax theory. These researches were aimed at developing a systematic variational approach to the equivariant periodic n-body problem in the two and three-dimensional space. The purpose of this paper is to expose the main problems and achievements of this approach. The material here was exposed in the talk that given at the Meeting CELMEC IV promoted by SIMCA (Società italiana di Meccanica Celeste).