关于一类Lagrange函数族的存在条件

研究力学系统的Lagrange函数族,根据从第一积分直接构造Lagrange函数的方法,提出一类Lagrange函数族的结构,导出这类Lagrange函数族的存在条件和直接构造方法.举例说明所得结果的应用.     

一类二阶非标准广义力学的正则变换和第一积分

研究带有指数Lagrange函数的二阶非标准广义力学的正则变换以及关于第一积分的Poisson理论. 首先, 建立二阶非标准广义力学的Hamilton原理,导出Euler Lagrange方程,并由Legendre变换定义Hamilton函数,建立正则方程; 其次, 建立二阶非标准广义力学的正则变换的判别条件, 并通过母函数的不同选择给出四种基本形式的正则变换; 最后, 验证二阶非标准广义力学具有Lie代数结构,建立关于第一积分的Poisson理论. 文中通过算例演示结果之应用.     

利用变量变换构造耗散系统Lagrange函数

提出变系数耗散系统变分法逆问题的一种间接解法.首先利用坐标和时间变量变换将系统运动微分方程化为自伴随方程,计算得到Lagrange函数后,再变换为原来变量以得到给定方程的Lagrange函数.给出两个例子以说明所得结果的应用.     

Lagrange函数族及其存在条件的再研究

再研究由第一积分组成Lagrange函数族的结构及其存在条件,指出同一个函数族有多种表示方式,并给出新形式的函数族的存在条件.     

一阶Lagrange力学逆问题的直接解法

提出求解一阶Lagrange力学逆问题的新途径;给出由一阶微分方程直接构造Lagrange函数的基本解法,以及几种与不同的补充条件相对应的特殊解法.举例说明所得结果的应用.     

从运动方程构造Lagrange函数的直接方法

根据对Lagrange函数的结构分析,提出直接从运动微分方程构造一维系统Lagrange函数新的一般方法和6种特殊方法.利用提出的方法导出若干运动微分方程的Lagrange函数.直接构造法证实一个系统具有多个不同而等效的Lagrange函数,甚至是Lagrange函数族.这种直接构造法也是构造Lagrange对称性并导出对应守恒量的一种途径.     

一阶系统自伴随条件和Lagrange函数的构造

重新研究一阶系统变分法逆问题,修正了某些文献关于一阶微分方程组自伴随条件的失误,导出了把一阶系统化为自伴随形式的变换矩阵所满足的方程,列出了构造自伴随一阶系统Lagrange函数的两种方法.举例说明所得结果的应用.     

导出变系数非线性动力学系统拉格朗日函数的两种方法

利用从运动微分方程出发和从第一积分出发导出拉格朗日函数的两种直接方法,构造变系数非线性动力学系统¨x+b(x)x~2+c(x)x=0的拉格朗日函数和c(x)=0特殊情况的拉格朗日函数族.另外,讨论了这种非保守系统广义能量守恒的物理意义.     

遗传算法在多修正因子寻优中的应用

模糊控制系统中的多修正因子校正法是一种方便、有效的控制规则优化方法,其修正因子的选取是一个寻优问题。常见的寻优方法有局部搜索法、模拟退火法和遗传算法。本文基于基本遗传算法,在目标函数的制定方面作了相应改进,并将其应用于上述修正因子的寻优。实验结果表明,该算法能有效求得多修正因子的优化解。     

一种新的自适应模糊规则的算法

本文基于模糊目标的隶属函数调整修正因子的方法．提出一种新的基于模糊目标的隶属函数自调整算法来在线调整模糊规则的修正因子．从而得出一种新的自调整模糊控制器的设计方法．应用该方法对一个典型的二阶系统进行仿真研究，结果表明其设计方案具有一定的忧越性．     

Multilinear Volterra equations of the first kind and some problems of control

Elements of the theory of the multilinear Volterra equations of the first kind relying on the notion of corresponding majorant (integral, differential, functional) equations were set forth. The relation between the simplest majorant equations and special problems of dynamic system control was demonstrated.     

Numerical solution of an integral equations system of the first kind by using an operational matrix with block pulse functions

This article proposes a simple efficient method for solving a Volterra integral equations system of the first kind. By using block pulse functions and their operational matrix of integration, a first kind integral equations system can be reduced to a linear system of algebraic equations. The coefficient matrix of this system is a block matrix with lower triangular blocks. Numerical examples show that the approximate solutions have a good degree of accuracy.     

A new analytical method for solving systems of Volterra integral equations

In this paper, a new modified homotopy perturbation method (NHPM) is introduced for solving systems of Volterra integral equations of the second kind. Theorems of existence and uniqueness of the solutions to these equations are presented. Comparison of the results of applying the NHPM with those of the homotopy perturbation method and Adomian's decomposition method leads to significant consequences. Several examples, including the system of linear and nonlinear Volterra integral equations, are given to demonstrate the efficiency of the new method.     

On the evaluation of stress intensity factors for a simple crack under parametric loading

Two analytical approaches for the evaluation of stress intensity factors at the tips of a single straight crack in plane isotropic elasticity under symmetric tensile loading along the crack edges including a parameter are considered. The first method leads to an ordinary differential equation for the stress intensity factor (or to a system of such equations) with respect to the loading parameter, whereas the second method leads to closed-form results for the related integral by using Laplace transform techniques. Several elementary transcendental functions, such as the exponential function, were used in the loading distribution for an illustration of the present approaches and related results are presented. The computer algebra system Maple V was also used together with Gröbner bases (for the derivation of the differential equations) and with definite integration (for the derivation of the closed-form formulae).     

A comparison of the method of averaging and Grobner's integral equation†

The method of averaging is compared to Grobner's method of integral equations as applied to a weakly non-linear periodic system of differential equations. The first and second approximation to the solutions of the differential equations via both techniques are shown to be equivalent.     

An expansion–iterative method for numerically solving Volterra integral equation of the first kind

Most integral equations of the first kind are ill-posed, and obtaining their numerical solution often leads to solving a linear system of algebraic equations of a large condition number. So, solving this system is difficult or impossible. For numerically solving Volterra integral equation of the first kind an efficient expansion–iterative method based on the block-pulse functions is proposed. Using this method, solving the first kind integral equation reduces to solving a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to solve any linear system of algebraic equations. To show the convergence and stability of the method, some computable error bounds are obtained. Numerical examples are provided to illustrate that the method is practical and has good accuracy.     

The numerical solution of fractional differential equations using the Volterra integral equation method based on thin plate splines

Finding the approximate solution of differential equations, including non-integer order derivatives, is one of the most important problems in numerical fractional calculus. The main idea of the current paper is to obtain a numerical scheme for solving fractional differential equations of the second order. To handle the method, we first convert these types of differential equations to linear fractional Volterra integral equations of the second kind. Afterward, the solutions of the mentioned Volterra integral equations are estimated using the discrete collocation method together with thin plate splines as a type of free-shape parameter radial basis functions. Since the scheme does not need any background meshes, it can be recognized as a meshless method. The proposed approach has a simple and computationally attractive algorithm. Error analysis is also studied for the presented method. Finally, the reliability and efficiency of the new technique are tested over several fractional differential equations and obtained results confirm the theoretical error estimates.

     

High-order scheme for determination of a control parameter in an inverse problem from the over-specified data

The problem of finding the solution of partial differential equations with source control parameter has appeared increasingly in physical phenomena, for example, in the study of heat conduction process, thermo-elasticity, chemical diffusion and control theory. In this paper we present a high order scheme for determining unknown control parameter and unknown solution of parabolic inverse problem with both integral overspecialization and overspecialization at a point in the spatial domain. In these equations, we first approximate the spatial derivative with a fourth order compact scheme and reduce the problem to a system of ordinary differential equations (ODEs). Then we apply a fourth order boundary value method for the solution of resulting system of ODEs. So the proposed method has fourth order accuracy in both space and time components and is unconditionally stable due to the favorable stability property of boundary value methods. Several numerical examples and also some comparisons with other methods in the literature will be investigated to confirm the efficiency of the new procedure.     

地基波动影响下非线性粘弹性桩的混沌运动分析

研究了在地基波动影响下非线性粘弹性桩中的混沌运动．假定桩体材料满足Leaderrnan非线性粘弹性本构关系,得到在轴向载荷作用下满足Winkler条件的地基土波动方程、桩与地基土耦合振动方程;利用Galerkin方法将非线性积分一微分方程简化,并进行了数值计算,揭示了非线性粘弹性桩包括混沌运动在内的动力学行为．     

积分法动态数据校正技术的研究

基于积分法的动态数据校正具有简单、快速和适于在线应用的优点。本文对积分法动态数据校正技术的原理及其应用方法进行了研究。研究结果表明,该方法不要求有状态空间模型,能够充分利用整个时间轴的时间冗余信息；但积分法中的区间长度对其校正精度有影响,因此,采用该方法进行校正时应首先确定适宜的区间长度。将积分法应用于常减压炼油装置拟稳态过程的数据校正,计算结果表明该方法的计算精度高于稳态数据校正。