Higher-Order Lagrangian Equations of Higher-Order Motive Mechanical System

In this paper, if the condition of variation δt=0 is satisfied, the higher-order Lagrangian equations and higher-order Hamilton's equations, which show the consistency with the results of traditional analytical mechanics, are obtained from the higher-order Lagrangian equations and higher-order Hamilton's equations. The results can enrich the theory of analytical mechanics.     

A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics

A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under irdinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finadly, an example is given to illustrate the application of the results.     

大学物理中几个常见超越方程解的渐近表示

简要介绍了布尔曼一拉格朗日级数,并推出了几个常见超越方程的解的渐近表示.     

有界空间中的非线性声学和收敛的积累解

在微扰近似下,拉格朗日体系下的一阶、二阶波动方程解是具势运动,应用拉格朗日变动参数法来寻求积累解。在一般情况下,二阶波的波动方程在半空间会出现各式各样的积累解,它们沿着3个坐标变量的方向都有积累,在理想介质中它们不满足辐射条件。本文的结果表明,在考虑到介质的非理想性之后,也只有沿着平面边界面法线方向有积累的积累解才满足辐射条件,因而是收敛的。      

新型低电压大变形微驱动器数值求解及仿真

针对横向加载单向变形MEMS静电微驱动器位移过小或驱动电压过大问题,提出一种基于纵横弯曲变形原理的硅基大位移低驱动电压静电驱动器模型;基于拉格朗日-麦克斯韦机电动分析力学,建立轴向横向同时加载的微驱动器动力方程;分析温度应力、静电调节力和轴向挤压力对轴向载荷的影响;基于龙格-库塔算法和有限差分法分别将横向分布载荷和轴向载荷等效转化为横向集中载荷;仿真得到变形同驱动电压、调节电压、轴向挤压量和温差的关系;结果显示当驱动电压仅为16 V时,位移高达10.861μm,远大于传统横向加载单向变形微驱动器的位移量.实验验证了仿真结果.     

温度对生物质热解过程中传热特性的影响

基于欧拉-拉格朗日方法,考虑热解过程中挥发分的析出和颗粒体积的变化,以上海市常见的绿化树种香樟树的树枝为实验材料,对固定床中生物质颗粒热解过程中温度对传热特性的影响进行了详细研究,利用开源软件OpenFOAM获得了反应器内不同热解阶段不同温度范围内颗粒数的分布,给出了不同温度下的有效传热系数及不同传热方式所占的比例.结果 表明:热解温度越高,有效传热系数降低,固体颗粒的平均比热容也逐渐降低;同时热解温度越高,辐射的换热量占比越大,而对流提供的热量占比则不断下降.     

Properties of Strange Matter in a Model with Effective lagrangian

The strange hadronic mater with nucleons,Λ-hyperons and Ξ-hyperons is studied by using an effective nuclear model in a mean-field approximation.The density and strangeness fraction dependence of the effective baryon masses as well as the saturation properties and stabilities of the strange hadronic matter are discussed.     

欧拉-拉格朗日系统的jet辛算法

研究了在欧拉-拉格朗日系统上的jet辛算法.证明了第二作者在1998年给出的一个离散的欧拉-拉格朗日(DEL)方程存在一个离散形式的几何结构,它沿着解是不变的,这个结构可以通过对离散的作用量函数求导得到.由此,可以给出此格式的jet辛性质.利用这个结构证明了与此DEL方程相关的离散Nother定理.最后,给出了一个欧拉-拉格朗日方程上的jet辛差分格式的数值算例,并与其它的差分格式进行了比较.     

Difference Discrete Variational Principle,Euler—Lagrange Cohomology and Symplectic,Multisymplectic Structures II：Euler—Lagrange Cohomology

In this second paper of a series of papers,we explore the difference discrete versions for the Euler-Lagrange cohomology and apply them to the symplectic or multisymplectic geometry and their preserving properties in both the Lagrangian and Hamiltonian formalisms for discrete mechanics and field theory in the framework of multiparameter differential approach.In terms of the difference discrete Euler-Lagrange cohomological concepts,we show that the symplectic or multisymplectic geometry and their difference discrete structure-preserving properties can always be established not only in the solution spaces of the discrete Euler-Lagrange or canonical equations erived by the difference discrete variational principle but also in the function space in each case if and only if the relevant closed Euler-Lagrange cohomological conditions are satisfied.     

准坐标下广义非保守系统Lagrange方程的积分因子与守恒定理

用积分因子方法研究准坐标下广义非保守系统Lagrange方程的守恒定理.列写系统的运动微分方程，给出它的积分因子的定义.研究守恒量存在的必要条件.建立系统的守恒定理及其逆定理，并举例说明结果的应用. 关键词： 准坐标 Lagrange方程 积分因子 守恒量     

声场中空化气泡的耦合振动及形状不稳定性的研究

计算了两个具有非球形扰动的气泡所组成系统的能量,并基于Lagrange方程得到了有声相互作用的非球形气泡的动力学方程和形状稳定性方程,研究了声场中非球形气泡间相互作用力对非球形气泡的形状不稳定性和气泡形状模态振幅的影响.研究结果表明声场中具有非球形扰动的气泡之间的耦合方式有两种:形状耦合模式和径向耦合模式,气泡之间的耦合方式取决于气泡形状扰动模态.由形状耦合及径向耦合产生的气泡之间的相互作用力能够改变单个气泡的形状不稳定及形状模态振幅,具体影响因素取决于声场驱动条件、气泡形状模态、相邻气泡的初始半径.     

On Form Invariance, Lie Symmetry and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

On Form Invariance,Lie Symmetry,and Three Kinds of Conserved Quantities of Generalized Lagrange's Equations

In this paper, the form invariance and the Lie symmetry of Lagrange's equations for nonconservative system in generalized classical mechanics under the infinitesimal transformations of group are studied, and the Noether's conserved quantity, the new form conserved quantity, and the Hojman's conserved quantity of system are derived from them. Finally, an example is given to illustrate the application of the result.     

非线性发展方程的Riemann theta 函数等几种新解

为了构造非线性发展方程的复合型无穷序列精确解, 获得了第二种椭圆方程的Riemann theta 函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bäcklund变换和解的非线性叠加公式, 借助符号计算系统 Mathematica, 以mKdV方程为应用实例, 构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta 函数、Jacobi椭圆函数、双曲函数、 三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解. 关键词： 第二种椭圆方程 Riccati方程 非线性发展方程 Riemann theta 函数无穷序列解     

经典力学中加速度相关的Lagrange函数

研究了加速度线性相关的Lagrange函数,在加速度项系数对称的条件下,Lagrange方程保持为二阶微分方程;给出了从运动方程构造加速度相关的Lagrange函数的方法;研究同一系统的加速度相关和加速度无关的Lagrange函数之间的关系.举例说明结果的应用. 关键词： Lagrange方程 加速度相关的Lagrange函数 广义力学 Lagrange函数的规范变换     

sine-Gordon型方程的无穷序列新解

通过下列步骤,获得了sine-Gordon型方程的新解.第一步、通过函数变换,把sine-Gordon方程与sinhGordon方程的求解问题转化为两种非线性常微分方程的求解问题.第二步、获得了两种非线性常微分方程与第一种椭圆方程的拟B?cklund变换.第三步、利用第一种椭圆方程的B?cklund变换与新解,构造了sine-Gordon型方程的无穷序列新解.     

Nizhnik-Novikov-Vesselov方程的无穷序列类孤子精确解

为了构造非线性发展方程的无穷序列类孤子精确解, 发掘第一种椭圆辅助方程的构造性和机械化性特点, 获得了该方程的一些新类型解和相应的 Bäcklund变换. 在此基础上利用符号计算系统Mathematica构造了Nizhnik-Novikov-Vesselov方程的 无穷序列类孤子精确解, 包括无穷序列光滑类孤子解、 无穷序列类尖峰孤立子解和无穷序列类紧孤立子解.     

Second kind integral equations for the first kind Dirichlet problem of the biharmonic equation in three dimensions

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.     

Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量

研究Chetaev型约束的相对运动动力学系统Nielsen方程的Noether对称性与Noether守恒量. 对Chetaev型约束的相对运动力学系统Nielsen方程的运动微分方程、Noether对称性定义和判据进行具 体的研究, 得到了Noether对称性直接导致的Noether守恒量的表达式. 最后举例说明结果的应用.