Isolated Periodic Orbits and Stability in Separable Potentials

A method for determining the main families of isolated periodic orbits and their characteristic exponents in planar potentials which are separated by a point transformation is proposed. Since these orbits are continued analytically with the same stability, these results are persistent under small perturbations. The method is applied to the two fixed centers problem, the Paul trap and the dipole expansion of an electrostatic potential. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mass-Weighted Symplectic Forms for the N-Body Problem

Mass-weighted symplectic forms provide a unified framework for the treatment of both finite and vanishingly small masses in the N-body problem. These forms are introduced, compared to previous approaches, and their properties are discussed. Applications to symplectic mappings, the definition of action-angle variables for the Kepler problem, and Hamiltonian perturbation theory are outlined This revised version was published online in July 2006 with corrections to the Cover Date.     

EJECTION–COLLISION ORBITS AND INVARIANT PUNCTURED TORI IN A RESTRICTED FOUR‐BODY PROBLEM

We study the motion of an infinitesimal mass point under the gravitational action of three mass points of masses μ, 1–2μ and μ moving under Newton's gravitational law in circular periodic orbits around their center of masses. The three point masses form at any time a collinear central configuration. The body of mass 1–2μ is located at the center of mass. The paper has two main goals. First, to prove the existence of four transversal ejection–collision orbits, and second to show the existence of an uncountable number of invariant punctured tori. Both results are for a given large value of the Jacobi constant and for an arbitrary value of the mass parameter 0<μ≤1/2. This revised version was published online in July 2006 with corrections to the Cover Date.     

An integrated wavelet concept of physical geodesy

For the determination of the earth's gravity field many types of observations are nowadays available, including terrestrial gravimetry, airborne gravimetry, satellite-to-satellite tracking, satellite gradio-metry, etc. The mathematical connection between these observables on the one hand and gravity field and shape of the earth on the other is called the integrated concept of physical geodesy. In this paper harmonic wavelets are introduced by which the gravitational part of the gravity field can be approximated progressively better and better, reflecting an increasing flow of observations. An integrated concept of physical geodesy in terms of harmonic wavelets is presented. Essential tools for approximation are integration formulas relating an integral over an internal sphere to suitable linear combinations of observation functionals, i.e. linear functionals representing the geodetic observables. A scale discrete version of multiresolution is described for approximating the gravitational potential outside and on the earth's surface. Furthermore, an exact fully discrete wavelet approximation is developed for the case of band-limited wavelets. A method for combined global outer harmonic and local harmonic wavelet modelling is proposed corresponding to realistic earth's models. As examples, the role of wavelets is discussed for the classical Stokes problem, the oblique derivative problem, satellite-to-satellite tracking, satellite gravity gradiometry and combined satellite-to-satellite tracking and gradiometry. Received: 28 February 1997 / Accepted: 17 November 1997     

A VARIATIONAL METHOD FOR COMPUTING POTENTIAL COEFFICIENTS USING DIFFERENT TYPES OF GRAVIMETRIC DATA

In this paper,a variational method is presented for solving theclassical gravimetric,satellite gravimetric and satellite altimetric mixed typeboudary value problem to obtain the potential coefficients.According to thisprinciple,classical gravimetric data（height measured by geometric levelling orheight triangulation）,satellite gravimetric data（height measured by satellitegeodesy technique）and satellite altimetric data can be used jointly to calculate thepotential coefficients.     

内蕴大地边值问题

提出内蕴大地边值问题,使得有可能利用重力场边界观测研究地球重力场的内蕴结构。文中构造了椭球问题的迭代逼近求解程式,并给出了具体解式。     

扩散波的时空反演与洪水实时预报技术

以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Ｑ（ｘ,ｔ）的同时反演计算扩散波波速Ｃ（ｘ,ｔ）和扩散系数Ｄ（ｘ,ｔ）,根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。     

Seismic frame design via inverse mode design of frame-ground systems

A two-step stiffness design procedure is developed for a moment-resisting planar frame supported by a prescribed two-dimensional finite-element ground-pile system. In the first step, a hybrid inverse eigenmode problem is formulated and its solution is derived in an analytical form. A difficulty resulting from the existence of multiple interface nodes is overcome by incorporating a deformation constraint into a set of linear equations for finding the lowest-mode displacements at the interface nodes and in the ground. In the second step, the fundamental natural frequency of the combined system and the lowest mode-strain ratios in the frame specified in the first step are regarded as the parameters for adjusting the mean peak seismic member-end strains to their specified values. If the fundamental natural frequency of the frame with a fixed-base happens to be close to that of the ground, a difficulty arises in the two-step stiffness design procedure because of an irregular response amplification and of the non-predominance of the lowest-mode components. A new practical design procedure of rapid convergence is proposed such that an initial design is found for a stiff ground and that a sequence of stiffness designs is generated with respect to a ground stiffness parameter without any differential coefficient of series expansion. The accuracy of the model utilized in this paper and the validity of the present stiffness design procedure are verified through time-history response analysis.     

Explicit solution of a free boundary problem for a nonlinear absorption model of mixed saturated-unsaturated flow

In wet soils, zones of saturation naturally develop in the vicinity of impermeable strata, surface ponds and subterranean cavities. Hydrology must be then concerned with transient flow through coexisting unsaturated and saturated zones. The models of advancing saturated zones necessarily involve a nonlinear free boundary problem.A closed-form analytic solution is presented for a nonlinear diffusion model under conditions of ponding at the surface. The soil water diffusivity is restricted to the special functional form D(θ) = a/(b − θ)², where θ is the water content field to be determined and a, b are positive constants. The explicit solution depends on a parameter C (determined by the data of the problem), according to two cases: 1 < C < C₁ or C ≥ C₁, where C₁ is a constant which is obtained as the unique solution of an equation. This result complements the study given in P. Broadbridge, Water Resources Research, 1990, 26, 2435–2443, in order to established when the explicit solution is available. The behavior of the bifurcation parameter C₁ as a function of the driving potential is studied with the corresponding limits for small and large values. Moreover, the sorptivity is proven to be continuously differentiable function of the variable C.