Global Solution of Dynamical Systems a Report to Z. Kopal, on what Followed Since

Two basic problems of dynamics, one of which was tackled in the extensive work of Z. Kopal (see e.g. Kopal, 1978, Dynamics of Close Binary Systems, D. Reidel Publication, Dordrecht, Holland.), are presented with their approximate general solutions. The ‘penetration’ into the space of solution of these non-integrable autonomous and conservative systems is achieved by application of ‘The Last Geometric Theorem of Poincaré’ (Birkhoff, 1913, Am. Math. Soc. (rev. edn. 1966)) and the calculation of sub-sets of ‘solutions précieuses’ that are covering densely the spaces of all solutions (non-periodic and periodic) of these problems. The treated problems are: 1. The two-dimensional Duffing problem, 2. The restricted problem around the Roche limit. The approximate general solutions are developed by applying known techniques by means of which all solutions re-entering after one, two, three, etc, revolutions are, first, located and then calculated with precision. The properties of these general solutions, such as the morphology of their constituent periodic solutions and their stability for both problems are discussed. Calculations of Poincaré sections verify the presence of chaos, but this does not bear on the computability of the general solutions of the problems treated. The procedure applied seems efficient and sufficient for developing approximate general solutions of conservative and autonomous dynamical systems that fulfil the PoincaréBirkhoff theorems. The same procedure does not apply to the sub-set of unbounded solutions of these problems.     

Approximate general solution of 2-degrees of freedom dynamical systems using `les solutions precieuses'

This paper presents the procedure of a computational scheme leading to approximate general solution of the axi-symmetric,2-degrees of freedom dynamical systems. Also the results of application of this scheme in two such systems of the non-linear double oscillator with third and fifth order potentials in position variables. Their approximate general solution is constructed by computing a dense set of families of periodic solutions and their presentation is made through plots of initial conditions. The accuracy of the approximate general solution is defined by two error parameters, one giving a measure of the accuracy of the integration and calculation of periodic solutions procedure, and the second the density in the initial conditions space of the periodic solutions calculated. Due to the need to compute families of periodic solutions of large periods the numerical integrations were carried out using the eighth order, variable step, R-K algorithm, which secured for almost all results presented here conservation of the energy constant between 10^-9 and 10^-12 for single runs of any and all solutions. The accuracy of the approximate general solution is controlled by increasing the number of family curves and also by `zooming' into parts of the space of initial conditions. All families of periodic solutions were checked for their stability. The computation of such families within areas of `deterministic chaos' did not encounter any difficulty other than poorer precision. Furthermore, on the basis of the stability study of the computed families, the boundaries of areas of `order' and `chaos' were approximately defined. On the basis of these results it is concluded that investigations in thePoincaré sections have to disclose 3 distinct types of areas of `order' and 2 distinct types of areas of `chaos'. Verification of the `order'/`chaos' boundary calculation was made by working out several Poincaré surfaces of sections. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于RPC近似核线约束的CE-1影像匹配方法

"嫦娥一号"(简称CE-1)是中国自主研制并发射的首个月球探测器,卫星搭载的传感器是一个三线阵CCD立体相机,其主要科学目标是获取月球表面三维影像。根据三线阵影像以及月面影像的特点,为了能够得到密集度较高且分布均匀的同名点对,采用了一种基于RPC近似核线约束的影像匹配方法,结果表明基于核线约束的影像匹配方法较之传统二维影像匹配总体耗时短且具有较高的精度与可靠性。     

基于无人机图像的密集匹配方法研究

本文提出了一种基于FAST算法的无人机图像密集匹配,使用FAST算法提取两图像的特征点,并使用归一化互相关算法实现两特征点点集的匹配,然后根据初匹配的结果采用RANSAC算法鲁棒地估算出基本矩阵和单应矩阵;采用极线约束和单应约束通过归一化互相关关系稳健匹配出所有点。实验表明,该密集匹配方法结果令人满意。     

大地电磁测深视电阻率和相位曲线之间近似互算方法及程序实现

介绍了大地电磁测深曲线中视电阻率曲线和相位曲线之间互相近似推算的原理和方法,并给出基于MATLAB平台的主要实现代码,为实测视电阻率曲线和相位曲线的编辑和处理提供了一种近似参考依据。     

视觉基本矩阵与摄影测量中相对方位元素的关系推导

数字摄影测量与计算机视觉（特别是计算机立体视觉）的研究内容十分相近。基本矩阵是计算机视觉领域里的一个重要概念,其求解的稳健性和精度将直接影响到三维重构的效果和意义。从两者研究的对象出发,找出了两者之间的内在联系,也即视觉基本矩阵F与相对方位元素求解公式之间的表达关系,这将对今后数字摄影测量和计算机视觉两门学科的交叉发展有重要意义。     

Approximate velocity formula over mobile sediment bed induced by velocity-skewed waves and current

A velocity formula is proposed for flow over a mobile sediment bed induced by velocity-skewed waves and current. The formula is obtained by a separation of waves and current velocities and requires seven free variables related to free stream velocity and sediment characteristics. The formula includes two parts:(1) a wave part consisting of the free stream velocity and defect function, which considers phase lead, wave boundary layer thickness, and mobile bed level, and(2) a current part, which ch...     

Envelope‐based pushover analysis procedure for the approximate seismic response analysis of buildings

An envelope‐based pushover analysis procedure is presented that assumes that the seismic demand for each response parameter is controlled by a predominant system failure mode that may vary according to the ground motion. To be able to simulate the most important system failure modes, several pushover analyses need to be performed, as in a modal pushover analysis procedure, whereas the total seismic demand is determined by enveloping the results associated with each pushover analysis. The demand for the most common system failure mode resulting from the ‘first‐mode’ pushover analysis is obtained by response history analysis for the equivalent ‘modal‐based’ SDOF model, whereas demand for other failure modes is based on the ‘failure‐based’ SDOF models. This makes the envelope‐based pushover analysis procedure equivalent to the N2 method provided that it involves only ‘first‐mode’ pushover analysis and response history analysis of the corresponding ‘modal‐based’ SDOF model. It is shown that the accuracy of the approximate 16th, 50th and 84th percentile response expressed in terms of IDA curves does not decrease with the height of the building or with the intensity of ground motion. This is because the estimates of the roof displacement and the maximum storey drift due to individual ground motions were predicted with a sufficient degree of accuracy for almost all the ground motions from the analysed sets. Copyright © 2013 John Wiley & Sons, Ltd.     

基于Matlab的控制网平差教学软件与应用

介绍了基于Matlab的控制网平差软件的功能和特点,并将该软件应用到《控制网平差程序设计》课程的教学过程以及实际工程的数据处理中,取得了良好的效果。     

测角网间接平差中近似坐标自动概算算法设计

在对测角网进行平差计算时,网中未知点平面坐标的概算是一个关键问题。针对测角网的特点,设计了测角网近似坐标自动概算的算法,用实例验证了算法的正确性及可靠性,避免了繁琐的手工近似计算过程,提高了数据处理的效率。