On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.     

Model of wind-generated ambient noise in stratified shallow water

In order to build a rapid ocean ambient noise model adapted for a stratified shallow water, a hybrid model of normal mode method (for far field) and ray method (for near field) is suggested which combines the advantages of both methods. Since the near field of wind-generated noise is not sensitive to the sound speed profile, the sound speed profile is regarded as a constant; which makes the model rapid and accurate. The simulation results are in agreement with those of the wave model.     

Effective Hamiltonian for the D'Alembert Planetary Model Near a Spin/Orbit Resonance

The D'Alembert model for the spin/orbit problem in celestial mechanics is considered. Using a Hamiltonian formalism, it is shown that in a small neighborhood of a p:q spin/orbit resonance with (p,q) different from (1,1) and (2,1) the 'effective' D'Alembert Hamiltonian is a completely integrable system with phase space foliated by maximal invariant curves; instead, in a small neighborhood of a p:q spin/orbit resonance with (p,q) equal to (1,1) or (2,1) the 'effective' D'Alembert Hamiltonian has a phase portrait similar to that of the standard pendulum (elliptic and hyperbolic equilibria, separatrices, invariant curves of different homotopy). A fast averaging with respect to the 'mean anomaly' is also performed (by means of Nekhoroshev techniques) showing that, up to exponentially small terms, the resonant D'Alembert Hamiltonian is described by a two-degrees-of-freedom, properly degenerate Hamiltonian having the lowest order terms corresponding to the 'effective' Hamiltonian mentioned above.     

First-order asymptotics for the eigenfrequencies of the Earth and application to the retrieval of large-scale lateral variations of structure

Summary . We present a variety of examples, showing systematic fluctuations as a function of angular order of measured eigenfrequencies for given normal modes of the Earth. The data are single station measurements from the GEOSCOPE network. Such fluctuations are attributed to departures from the lowest order asymptotic expression of the geometrical optics approximation. We derive first-order asymptotic expressions for the location parameter for all three components of the Earth's motion, by a method based on the stationary phase approximation and geometric relations on the unit sphere.
We illustrate the sensitivity of the fluctuations to the different parameters involved (source parameters, epicentral distance, laterally heterogeneous earth model) with synthetic examples corresponding to GEOSCOPE observations. Finally, we show the results of first attempts at inversion, which indicate that, when the fluctuations are taken into account, more accurate estimates of the great circle average eigenfrequencies can be obtained, and additional constraints put on the structure in the neighbourhood of the great circle.     

The additive logistic skew-normal distribution on the simplex

There is a dearth of suitable models with which to adequately model compositional data sets, especially those which exhibit skewness after additive logratio-transformation. In order to address this deficit we propose the additive logistic skew-normal distribution, an extension to the additive logistic normal model on the simplex derived from the skew-normal distribution in real space. The purpose of this paper is to outline the potential of this distribution in the modelling of compositional data. We present its most important properties and use an example to exhibit the potential of this distribution.     

On the character of distribution of chemical elements in nature

Distribution of chemical elements in nature is controlled by the general physical-chemical state of natural processes, a result of the effort to reach thermodynamic equilibrium. Natural processes, forming geologic objects (e.g., rocks, ores) usually do not reach total chemical equilibrium. This is reflected in distributions of chemical elements in nature. We recognize symmetric as well as asymmetric distributions. The question arises, what distribution in nature is most commonly followed? Evidently, this should be a distribution of chemical elements in thermodynamic equilibrium throughout the system, thus with maximum entropy. This paper notes that Gauss's normal distribution may be derived from statistic explanation of entropy as a function of contnt of chemical elements in a system with application of Einstein's formula.     

茂名城区GPS拟合高程精度的探讨

GPS控制网在联测水准点的基础上,利用GPS水准高程来实现GPS网点的大地高向正常高转换,其精度主要受所拟合的似大地水准面、已知点高程和GPS网点大地高3种误差的影响。     

计算转换参数提高手持式GPS接收机定位精度的方法与探讨

通过在矿区施测的静态GPS控制测量,根据实际不同的坐标系工程用图需要,在矿区内均匀选择三个以上公共点的两套坐标,探讨对手持式GPS接收机求取其转换参数的方法,采用五参数转换法,求出转换参数,然后在手持GPS接受机上设置五参数来提高定位精度.     

样条函数拟合GPS高程探讨

主要讨论了运用三次样条函数曲线拟合法来拟合GPS点的高程,并与多项式曲线拟合法比较,通过实例验证了此方法的可行性及其所能达到的精度,得出了一些有益的结论,并给出了一些建议。     

铁岭县GPS控制网高程拟合精度分析

利用GPS技术测量点的平面位置可获得较高精度,但不能直接得到地面点的正常高,只能得到大地高。作者探讨了GPS高程拟合的精度与起算点的分布、整体拟合和分区拟合方法的选择、GPS高程拟合精度的分析等方法并提出了自己的见解,且通过铁岭县C级GPS网的高程拟合实例,介绍了该方法的具体应用。