一类偏微分方程的Hamilton正则表示

主要给出一系列关于力学中的偏微分方程的无穷维Ｈａｍｉｌｔｏｎ正则表示．其中包括变系数线性偏微分方程,ＫｄＶ方程,ＭＫｄＶ方程,ＫＰ方程,Ｂｏｕｓｉｎｅｓｑ方程等的无穷维Ｈａｍｉｌｔｏｎ正则表示．     

一类偏微分方程的Hamilton正则表示1)

主要给出一系列关于力学中的偏微分方程的无穷维Hamilton正则表示.其中包括变系数线性偏微分方程,KdV方程, MKdV方程, KP方程,Boussinesq方程等的无穷维Hamilton正则表示.     

球面各向同性弹性力学的位移解法

本文引入三个位移函数（ｗ，Ｇ，ψ），将球面各向同性弹性力学运动方程，简化为关于ψ的二阶偏微分方程，和关于Ｗ和Ｇ的联立方程。在静力学问题中，联立方程可进一步简化，ｗ和Ｇ可用另一位移函数Ｆ表示，而Ｆ满足一个四阶偏微分方程。在球壳固有振动问题中，则简化为一个独立的二阶常微分方程，和另两个二阶的联立的常微分方程，证明了在多层球壳中，它们分别对应独立的两类振动。改进了常微分方程的解法，并计算了一个二层球壳的频率。     

非力学系统的对称性与守恒量(Ⅱ)──分析力学札记之八

将非力学系统的微分方程化成Ｈａｍｉｌｔｏｎ方程形式,引进无限小变换,研究微分方程或Ｈａｍｉｌｔｏｎ作用量在无限小变换下的不变性,进而给出守恒量存在的条件以及守恒量的形式．     

含初缺陷复合材料圆柱曲板的动力屈曲分析

基于修正的一阶剪切变形理论，利用Ｈａｍｉｌｔｏｎ原理导出包含横向剪切变形和转动惯量的复合材料长圆柱曲板的非线性动力方程，通过将位移和载荷展开为Ｆｏｕｒｉｅｒ级数，把非线性偏微分方程组转化为二阶常微分方程组，并可由四阶Ｒｕｎｇｅ－Ｋｕｔｔａ方法数值求解，通过算例，讨论了有关因素对迭层复合材料圆柱曲板动力屈曲的影响。     

非力学系统的对称性与守恒量(I)——分析力学札记之七

将非力学系统的微分方程化成Ｌａｇｒａｎｇｅ方程形式,引进无限小变换,研究微分方程或Ｈａｍｉｌｔｏｎ作用量在无小变换,研究微分方程或Ｈａｍｉｌｔｏｎ作用量在无限小变换下的不变性,进而给出守恒量存在的条件以及守恒量的形式。     

Hamilton原理四种表达形式的异同

Ｈａｍｉｌｔｏｎ原理四种表达形式的异同陈滨（北京大学力学系北京１００８７１）１．引言Ｈａｍｉｌｔｏｎ原理是经典力学中的重要原理。它是以泛函（Ｈａｍｉｌｔｏｎ作用量）驻值的变分形式给出的力学系统动力学原理,并可以作为整个力学系统动力学研究的基础,Ｈａｍ...     

Hamilton体系下弹性力学的两个守恒律

采用与前稍有不同的方法,将Ｈａｍｉｌｔｏｎ体系引入弹性力学中,并讨论了相应的Ｈａｍｉｌｔｏ函数的守恒性和动量守恒定律,从而丰富了弹性力学的Ｈａｍｉｌｔｏｎ求解体系。     

弹性力学平面问题的位移型解答

本文证明了一个线性常系数偏微分方程的通解定理,利用这个通解定理导出了弹性力学平面问题的位移通解。     

三广义位移平板弯曲问题的康托洛维奇—加权残值法

固体力学问题最后都可归结为求解偏微分方程的边值问题,一般情况下难以求出其精确解。本文对几种问题,用 kantorovich 近似变分法将问题转化成为求解常微分方程的 Euler-poisson 方程(组),再用加权残值法求解。概念清晰,思路明确。     

Oscillation of solutions for a class of nonlinear neutral parabolic differential equations boundary value problem

ＩｎｔｒｏｄｕｃｔｉｏｎＤｕｅｔｏｔｈｅａｃｃｕｒｅｎｃｅｏｆａｇｒｅａｔｄｅａｌｏｆｍａｔｈｅｍａｔｉｃｍｏｄｅｌｌｉｎｇｓｄｅｓｃｒｉｂｅｄｉｎｐａｒｔｉａｌｆｕｎｃｔｉｏｎａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓｉｎｔｈｅａｐｐｌｉｃａｔｉｏｎｆｉｅｌｄｓｏｆｍｅｃｈａｎｉｃｓａｎｄｃｏｎｔｒｏｌｔｈｅｏｒｙ[1],ｇｒｅａｔｉｎｔｅｒｅｓｔｗａｓａｒｏｕｓｅｄａｓｔｏｔｈｅｓｔｕｄｉｅｓｏｎｔｈｅｐｒｏｐｅｒｔｙｏｆｔｈｅｓｏｌｕｔｉｏｎｓｏｆｔｈｉｓｔｙｐｅｏｆｅｑｕａｔｉｏｎｓ.Ｇ…     

Construction of Basis Functions and Their Application to Boundary-Value Problems of Mechanics of Continuous Media

A unified method for constructing basis (eigen) functions is proposed to solve problems of mechanics of continuous media, problems of cubature and quadrature, and problems of approximation of hypersurfaces. Numerical-analytical methods are described, which allow obtaining approximate solutions of internal and external boundary-value problems of mechanics of continuous media of a certain class (both linear and nonlinear). The method is based on decomposition of the sought solutions of the considered partial differential equations into series in basis functions. An algorithm is presented for linearization of partial differential equations and reduction of nonlinear boundary-value problems, which are reduced to systems of linear algebraic equations with respect to unknown coefficients without using traditional methods of linearization.     

EXISTENCE THEOREMS OF SOLUTIONS FOR TWO－POINT BOUNDARY VALUE PROBLEM OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

ＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＳＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＷＯ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＯＦＳＥＣＯＮＤＯＲＤＥＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＩＮＢＡＮＡＣＨＳＰＡＣＥＳＺｈａｎｇＳｈｉｓ...     

Inhomogeneous initial-boundary value problem for Ginzburg-Landau equations

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.     

流固耦合介质轴对称动力问题解法的改进

用直接求解常微分方程组解文［１］所得的控制方程，减少了传递矩阵计算工作量，避免了子阵求逆，使问题的求解得到了简化     

Asymptotic Solution for a Kind of Boundary Layer Problem

This paper studies the partial differential equation with a small coefficient in the highest-order item. This kind of equation is also named as boundary layer problem. The Burgers equation and modified Burgers equation are analyzed in this approach. First, these equations are transferred into the strong nonlinear ones, and then the corresponding strong nonlinear equations are solved based on the perturbation method. The results from the asymptotic method are comparable with those obtained from numerical computation. An erratum to this article is available at .     

压电陶瓷中圆币形裂纹在横向剪力下的机－电耦合行为

以弹性位移分量和电势函数为基本未知量时，横观各向同性压电介质三维问题的场方程可化为四个联立的二阶线性偏微分方程组，本文导出了用四个调和函数表示位移分量及电势函数的表达式，即得到了该场方程的势函数通解，作为通解的应用举例，文中求解了圆币形裂纹受横向剪切作用的问题，得到了裂尖附近应力场及电位移场的解析表达式，结果表明，在横向剪切载荷下圆币形裂纹的尖端场及应力、电位移强度因子均具有明显的机－电耦合性质，而应力和电位移分量在裂尖仍具有－１／２的奇异性。     

Timoshenko固端梁特征值问题近似计算方法

利用模态摄动法将Timoshenko梁特征值问题的求解转化为一组非线性代数方程组的求解，不仅可以简化计算过程，而且计算结果具有较高的精度，对同一类问题具有适用性。通过算例，计算了在不同长细比条件下，剪切变形和转动惯量对固端梁的各阶主频率的影响。     

A stability study of Navier-Stokes equations (III)

In this paper, the necessary conditions of the existence of C² solutions in some initial problems of Navier-Stokes equations are given, and examples of instability of initial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equation various authors studies this problem and contributed a number of results. J. Lerav, a French professor, proved the existence of Navier-Stokes equation under certain defined initial and boundary value conditions. In this paper, with certain rigorously defined key concepts, based upon the basic theory of J. Hadamard partial differential equations¹, gives a fundamental theory of instability of Navier-Stokes equations. Finally, many examples are given, proofs referring to Ref. [4].