一类Painleve方程的Lagrange函数族

利用第一积分构造Lagrange函数的理论和方法, 导出一类Painleve方程的两个Lagrange函数族, 以及一些Lagrange函数和Hamilton函数.     

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     

线性三原子分子振动的Lagrange函数和Hamilton函数

本文以线性耦合振子为模型,导出了三种不同坐标变量表示下线性对称三原子分子的振动微分方程,利用分析力学逆问题理论和方法,构造出了五种对应的Lagrange函数和Hamilton函数,其中有些是新的结果.     

计算加速度相关Lagrange函数的方法

研究从运动微分方程构造加速度相关Lagrange函数的问题,给出一种由方程的自伴随形式计算加速度相关Lagrange函数的方法.举例说明结果的应用. 关键词： 分析力学 加速度相关Lagrange函数 自伴随性 Lagrange力学逆问题     

单个守恒型方程熵耗散格式中熵耗散函数的构造

对于一维单个守恒律方程,文[8]设计了一种非线性守恒型差分格式.此格式为二阶Godunov型的,用的是分片线性重构(reconstruction),重构函数的斜率是根据熵耗散得到的.格式满足熵条件.与传统的守恒格式不同的是此格式在计算过程中不仅用到了数值解还用到了数值熵.在此格式中一个所谓的熵耗散函数起到了很重要的作用,它在每一个网格的计算中耗散熵,以保证格式满足熵条件.文[8]中设计的熵耗散函数比较复杂,并且不是很完善.故数值地分析了在格式的构造中为何应给熵以一定的耗散,及应耗散多少.并且给出了一个新的以数值解的二阶差分作为基本模块的熵耗散函数.最后给出了相应的数值算例.     

阻尼耦合振动的Lagrange函数和Hamilton函数

本文研究两种阻尼耦合振动的分析力学化.首先,利用坐标变换将方程变换成自伴随形式;其次,根据Engels方法计算得到Lagrange函数;最后,由逆变换导出原始方程的Lagrange函数,以及Hamilton函数.     

相对论热力学的哈密顿函数

Planck-Einstein的相对论热力学理论一直存在着争议,特别是它是否遵守动量－能量守恒定律,本文从热力学的Lagrange函数,导出了对应的Hamilton函数,Hamilton函数的意义极为明确,它包含了环境对体系作用的耦合能量,在一般情况下,不是体系的能量,而是Hamilton量,和动量组成了四维矢量,这不仅证明了P－E理论是符合守恒定律的,而且扩展了这一理论。     

关联函数在耗散反应激发函数涨落中的应用

应用关联函数方法,分析耗散反应激发函数中的涨落.通过推导出能量自关联函数、角度互关联函数、反应产物元素之间的互关联函数、反应产物同位素之间的互关联函数,来分析在耗散反应这一由非平衡向平衡演化的系统中,核反应体系演化过程的特点,说明关联函数在研究耗散反应激发函数涨落中的特殊作用.用推导出的函数分析了实验4.5MeV/u ²⁷Al+²⁷Al和102.5MeV ¹⁹F+⁵¹V的数据,并且指出了用这种方法可以提取的耗散反应体系的信息.     

部分线性的分数阶混沌系统修正函数投影同步

针对一类部分线性的分数阶混沌系统修正函数投影同步问题, 可通过单变量耦合构造出这类系统的响应系统, 从而提出修正函数投影同步的设计方法. 根据Routh-Hurwitz条件, 给出耦合部分线性系统实现修正函数投影同步的方法, 并设计了控制器. 该方法中控制器和误差动态方程的选择都是确定的, 理论分析和数值仿真都说明了该方法在部分线性的分数阶混沌系统中应用具有可行性和有效性. 关键词： 分数阶混沌系统 部分线性 修正函数投影同步     

SPH二阶粒子近似光滑函数的充分条件及数值验证

为实现SPH二阶粒子近似,讨论光滑函数应满足的充分条件,给出对应的光滑函数形式,分析二阶粒子近似解的唯一性,并进行数值验证.结果表明：和标准SPH方法相比,在周期边界条件下,随着粒子数加密,SPH方法二阶粒子近似的L₁误差减小且L₁阶趋近2.0.     

构造准正则变换的方法

给出构造Hamilton系统的准正则变换的方法,首先将Hamilton系统变换成Birkhoff系统,然后将Birkhoff系统作规范变换并实现Hamilton化. 指出对一个Hamilton系统存在多种准正则变换. 举例说明所得结果的应用. 关键词： Hamilton系统 准正则变换 Birkhoff系统 规范变换     

A set of the Lie symmetrical conservation laws for the rotational relativistic Birkhoffian system

For a rotational relativistic Birkhoffian system a set of the Lie symmetries and conservation laws is given under infinitesimal transformation. On the basis of the invariance of rotational relativistic Birkhoffian equations under infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetries are given, and a new type of non-noether conserved quantities are directly obtained from Lie symmetries of the system. An example given to illustrate the application of the results.     

Lie Symmetrical Perturbation and Adiabatic Invariants of Generalized Hojman Type for Relativistic Birkhoffian Systems

For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.     

Birkhoffian Symplectic Scheme for a Quantum System

In this paper, a classical system of ordinary differential equations is built to describe a kind of n-dimensional quantum systems. The absorption spectrum and the density of the states for the system are defined from the points of quantum view and classical view. From the Birkhoffian form of the equations, a Birkhoffian symplectic scheme is derived for solving n-dimensional equations by using the generating function method. Besides the Birkhoffian structure- preserving, the new scheme is proven to preserve the discrete local energy conservation law of the system with zero vector f . Some numerical experiments for a 3-dimensional example show that the new scheme can simulate the general Birkhoffian system better than the implicit midpoint scheme, which is well known to be symplectic scheme for Hamiltonian system.     

Whittaker Order Reduction Method of Relativistic Birkhoffian Systems

The order reduction method of the relativistic Birkhoffian equations is studied. For a relativistic autonomous Birkhoffian system, if the conservative law of the Birkhoffian holds, the conservative quantity can be called the generalized energy integral. Through the generalized energy integral, the order of the system can be reduced. If the relativistic Birkhoffian system has a generalized energy integral, then the Birkhoffian equations can be reduced by at least two degrees and the Birkhoffian form can be kept. The relations among the relativistic Birkhoffian mechanics, the relativistic Hamiltonian mechanics and the relativistic Lagrangian mechanics are discussed, and the Whittaker order reduction method of the relativistic Lagrangian system is obtained. And an example is given to illustrate the application of the result.     

Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the R-matrices for two-component systems under these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin‘s formalism.For those R-matrices with all required properties,the effects of solution transformations to the six-and eight-vertex systems with open boundary conditions are discussed.these effects can be one of the following types:the Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.     

转动系统相对论性Birkhoff动力学的基本理论

建立转动系统相对论性Birkhoff动力学的基本理论,给出其Birkhoff函数和Birkhoff函数组、Pfaff作用量、Pfaff-Birkhoff原理、Pfaff-Birkhoff-D’Alembert原理,以及Birkhoff方程.并研究转动系统相对论性Lagrange力学、Hamilton力学与转动系统相对论性Birkhoff动力学之间的关系,证明完整保守、完整非保守转动相对论系统都可纳入转动相对论Birkhoff系统 关键词： 转动系统 相对论 Birkhoff动力学 变分原理     

Hojman Conservation Laws for Relativistic Birkhoffian System

For a relativistic Birkhoffian system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhoffian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results.     

Hojman Conservation Laws for Relativistic Birkhoffian System

For a relativistic Birkhoman system, the Lie symmetry and Hojman conserved quantity are given under infinitesimal transformations. On the basis of the invariance of relativistic Birkhottian equations under infinitesimal transformations, Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The determining equations of Lie symmetry are given, and a Hojman conserved quantity is directly obtained from Lie symmetry of the system. An example is given to illustrate the application of the results.     

Constructing the time independent Hamiltonian from a time dependent one

In this paper we introduce a method for finding a time independent Hamiltonian of a given Hamiltonian dynamical system by canonoid transformation of canonical momenta. We find a condition that the system should satisfy to have an equivalent time independent formulation. We study the example of a damped harmonic oscillator and give the new time independent Hamiltonian for it, which has the property of tending to the standard Hamiltonian of the harmonic oscillator as damping goes to zero.