初轨计算中的病态分析

本文对现有初轨计算方法进行病态性分析与误差分析；研究结果表明：病态对现有初轨算法的影响，主要来源于法方程系数中包含观测误差．系数行列式愈大，定轨精度的损失愈多，当■被随机误差项△μ淹盖时，现有初轨算法将失效．此外，仿真结果还显示：■与△μ的大小还极大地依赖观测弧段的空间位置，当观测弧段包含近站点作为中点时，■最大，而■小，此时定轨精度较高；当观测弧段位于近站点的某一侧时，■小，而■大，此时定轨精度较低，观测弧段愈偏离近站点，病态影响愈大；因而在观测时，应尽量使观测弧段与近站点对称（此时μ值较大），这是提高短弧定轨的一种有效途径．     

On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.     

On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

有关边界层问题中一类奇异积分方程新的存在性结果

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。     

INITIAL SEDIMENTATION OF WASTE PARTICLES DISCHARGED IN COASTAL WATERS

Based on a puff model . and together with the consideration of convection , dispersion and descent of suspended waste particles in marine environment , a numerical model is presented to predict the initial sedimentation of waste particles discharged from ocean outfalls in coastal waters and to compute the stable sedimentation rate in homogeneous trde current fields with water depth constant . When the time step selected is small enough , the results from this model agree well with that from the semi-analytical solution , and have sufficient precision for evaluating the impact on the environment caused by sedimentation of waste particles discharged from ocean outfalls. A numerical example is given for predicting the sedimentation of waste particles discharged in Heishijiao , Dalian .     

On The Concept Of Periapsis In Hill’s Problem

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.     

BACKGROUND STUDY ON NON-RESIDUAL PHASE OF ELEMENTS IN CHANGJIANG AND HUANGHE ESTUARINE SEDIMENTS

Analysis of Zn, Cu, Pb, Co, Cr, Li, Ni, K, Al, Fe extracted by 1 mol/L HCl or 0.5 mol/LHCl/H_2O_2, showed concentrations of Zn, Cu, Pb, Co, Cr, Fe, Ni were significantly correlated with Li, Al,K, and clay. Two methods are used to indicate the background value of the non-residual phase of elementsin sediments, and are the same as the methods used to indicate the background value of totalconcentrations in sediments. The first method uses correlograms and regression equations,the second usesthe mean element concentrations normalized with grain size. Li, Al, K can be used as reference elements to determine the background value of Zn, Cu, Pb, Co,Cr, Ni, Fe, while the clay concentration's correlation with some extractable concentrations can be used tocalculate the background value of the non-residual phase of elements as a percentage of clay concentrationin the sediments. Based on this study, the concept of using the background value of the non-residualphase of elements to compare the pollution level in differ     

Boundary curves for families of planar orbits

For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.     

Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.     

Robe's restricted three-body problem revisited

Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.