地球重力场、重力、重力梯度在三维直角坐标系中的表达式

现代卫星重力测量主要利用星载GPS接收机、加速度计、星载测距仪等来确定重力卫星的轨道 ,削弱非保守力的干扰 ,由此根据卫星的位置、速度及其变率来确定地球重力场。而上述GPS等星载仪器所提供的数据 ,包括卫星轨道坐标及其速率、扰动加速度、星间距离及其变率 ,都是以三维直角坐标 (x ,y ,z)的形式表示的 ,因此 ,地球重力场。

三维直角坐标系下三环网络的超L型瓦仿真

传统的超L型瓦仿真算法主要采用穷举的方法,效率较低,且有一定的局限性。针对上述问题,将三维直角坐标系引入三环网络,在三维直角坐标系下,提出广义三环网络G(N;s1,s2,s3)的超L型瓦仿真算法,利用C++和OpenGL实现超L型仿真,并求得其相关参数l、m、n,以及三环网络的直径D。实验结果表明,该算法具有较高的执行效率和更强的通用性。

四至七维空间直角坐标系的三维模型建立及其应用

本文从n维空间有限旋转群理论出发,证明了n维空间正则立体的存在,着重研究了n维空间立方体的情况,得到四至七维空间直角坐标系在三维空间的投影模型,并将其应用到几何和物理模型的制作方面。

已知参数的平板折叠桌的动态变化模型和设计加工模型

在合理的假设和规定下,通过建立三维直角坐标系,本文建立了已知参数的平板折叠桌的动态变化模型和设计加工模型。

Self-Similar Solutions of Three-Dimensional Navier-Stokes Equation

In this article we will present pure three dimensional analytic solutions for the Navier-Stokes and the continuity equations in Cartesian coordinates. The key idea is the three-dimensional generalization of the well-known self-similar Ansatz of Barenblatt. A geometrical interpretation of the Ansatz is given also. The results are the Kummer functions or strongly related. Our final formula is compared with other results obtained from group theoretical approaches.

Seismic Waves in a Layered Half-Space from an Arbitrary Buried Source

In this paper, a transfer matrix and a three-dimensional dynamic response of a layered half-space to an arbitrary buried source are derived with the aid of a technique which combines the Laplace and two-dimensional Fourier transforms in a rectangular coordinate system. This method is clear in concept, and the corresponding formulas given in the paper are simple and convenient for marine seismic prospecting and other fields' applications. An example is presented and the calculated results are in good agreement with those of the finite element method (FEM).

A Computer Modeling of the China Central Television Headquarters in Beijing

This paper deals with the computer modeling of structures starting from a point cloud. The CCTV （China Central Television） tower headquarters is the case for study because the shape of this building is non-stellar, concave and multi-connected. It is composed of sowns and chains. The sown is the representation of a horizontal plane formed by dense points. The chain is a planar path modeled by rare points. The CCTV structure is defined only by the three orthogonal Cartesian coordinates of the points. The proposed computer modeling uses a sequence of procedures and the desired outputted 3D model is consistent. The first procedure is devoted to attributing points to their voxel and to estimating three values needed afterwards. The second procedure is devoted to analyzing clusters vertically and horizontally, to preliminarily distinguishing chains from sowns and to generating relational matching. The third procedure is devoted to building closed paths between all chains and all their projections on sowns. The fourth procedure is devoted to connecting points with triangles. The fifth procedure, still being implemented, is devoted to interpolating triangles with triangular splines. The results show it is possible to achieve the 3D model using the above mentioned procedures. These procedures are written, implemented and tested and they form a library of people＇s own software. The code is written using Matlab. It is not possible to obtain the required 3D model if the procedures are applied in the wrong order or one step is skipped. To conclude, it is possible to obtain the computer model of the CCTV using the provided sequence of procedures.

一种适用于局部重力场的傅里叶表达式

本文从局部重力场在直角坐标系下的最基本原理边值问题出发,讨论了边值问题在二维和三维直角坐标系下的求解过程,得出了适用于局部重力场的普通解的傅里叶级数表达式;根据傅里叶表达式中三角函数的正交性,得出了其傅里叶系数的积分表达式;根据大地测量学中各物理量之间的关系,分别求得了重力异常和重力梯度垂直分量在二维直角坐标下的傅里叶系数关系式,以及重力场扰动位和重力异常、重力场扰动位及其重力梯度分量在三维直角坐标下的傅里叶系数关系式,并根据实际算例验证了上述表达式的有效性。

Construction of homogeneous loading functions for elastoplastic damage models for concrete

Over the past 2 decades,tight restriction has been imposed on strength criteria of concrete by the combination of plasticity and damage in one theory.The present study aims at constructing plastic/damage loading functions for elastoplastic damage models for concrete that can perform more satisfactorily in 3D stress states.Numerous strength criteria of concrete are reorganized according to their simplest representations as Cartesian,cylindrical,mixed cylindrical-Cartesian,and other forms,and the homogeneity of loading functions discussed.It is found that under certain supplementary conditions from physical meanings,an unambiguous definition of the cohesion in a strength criterion,which is demanded in an elastoplastic damage model,is usually available in an explicit or implicit form,and in each case the loading function is still homogeneous.To apply and validate the presented theory,we construct the respective homogeneous damage and plastic loading functions and implant them into some widely used elastoplastic damage models for concrete,and their performances in triaxial compression prove to have improved significantly.