Symmetries and Two Types of Non-Noether Conservation Laws of Birkhoffian System with Unilateral Constraints

The symmetries and non-Noether conservation laws of Birkhoffian system with unilateral constraints are studied. The differential equations of motion of the system are established, and the criterions of Noether symmetry, Lie symmetry and Mei symmetry of the system are given. Two types of new conservation laws, called the Hojman conservation law and the Mei conservation law respectively, are obtained, and the intrinsic relations among the symmetries and the new conservation laws are researched. At the end of the paper, an example is given to illustrate the application of the results.     

大尺度三维几何尺寸立体视觉测量系统实现

基于立体视觉的大尺度三维几何尺寸测量技术是对外形不规则的大型物体进行几何量测量的有效方法。与传统的视觉测量技术不同,大尺度视觉测量的精度随测量距离的增加而迅速下降,同时大尺度空间下照明条件难以控制,也使得测量变得不稳定。因此如何在大测量尺度的前提下提高测量精度成为这一领域的研究难点。从立体视觉测量系统的原理出发,分析了影响系统精度的各种因素,将相位一致性变换与极线约束条件引入结构光光条中心提取之中,显著提高了图像分析的精度。研制了测量系统的样机并给出了实验结果,现场测试表明该系统可以有效地保证大尺度条件下的测量精度。     

利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束     

相空间中单面完整约束力学系统的对称性与守恒量

在增广相空间中研究单面完整约束力学系统的对称性与守恒量.建立了系统的运动微分方程；给出了系统的Norther对称性，Lie对称性和Mei对称性的判据；研究了三种对称性之间的关系；得到了相空间中单面完整约束力学系统的Noether守恒量以及两类新守恒量——Hojman守恒量和Mei守恒量，研究了三种对称性和三类守恒量之间的内在关系.文中举例说明研究结果的应用. 关键词： 分析力学 单面约束 对称性 守恒量 相空间     

多体系统动力学方程违约修正的数值计算方法

多体系统动力学方程为微分代数方程,一般将其转化成常微分方程组进行数值计算,在数值积分的过程中约束方程的违约会逐渐增大.本文对具有完整、定常约束的多体系统,在修改的带乘子Lagrange正则形式的方程的基础上,根据Baumgarte提出的违约修正的方法,给出了一种多体系统微分代数方程违约修正法和系统的动力学方程的矩阵表达式.通过对曲柄-滑块机构的数值仿真,计算结果表明本文给出的方法在计算精度和计算效率上好于Baumgarte提出的两种违约修正的方法.     

HIRFL与CSR的匹配研究

国家重大科学工程HIRFLCSR冷却储存环计划主环CSRm利用已有的HIRFL作为注入器,为了更好地利用HIRFL加速器的能力,对这两台加速器的匹配在原来的初步考虑的基础上进行了较为详细的研究,提出了分别利用HIRFL自己的注入器SFC单独注入到CSR以及SFC加上主加速器SSC注入到CSR的两套方案,既可以提高HIRFL与CSR的总传输效率,又可以在SFC与CSR联合运行的同时使SSC与另建的小回旋加速器组合加速质子,从而充分提高HIRFL的运行效率.     

Hamiltonian Systems and Darboux Transformation Associated with a 3 × 3 Matrix Spectral Problem

Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potentials and the eigenfunctions, Lax pair and adjoint Lax pairs including partial part and temporal part are nonlinearied into two finitedimensional Hamiltonian systems (FDHS) in Liouville sense. Moreover, an explicit N-fold Darboux transformation for CDNS equation is constructed with the help of a gauge transformation of the spectral problem.     

Stability and vibration of a helical rod constrained by a cylinder

The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler’s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov’s and Euler’s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form. The project supported by the National Natural Science Foundation of China (10472067). The English text was polished by Yunming Chen.     

MPCC: on necessary conditions for the strong stability of C-stationary points

ABSTRACT

We consider the concept of strongly stable C-stationary points for mathematical programs with complementarity constraints. The original concept of strong stability was introduced by Kojima for standard optimization programs. Adapted to our context, it refers to the local existence and uniqueness of a C-stationary point for each sufficiently small perturbed problem. The goal of this paper is to discuss a Mangasarian-Fromovitz-type constraint qualification and, mainly, provide two conditions which are necessary for strong stability; one is another constraint qualification and the second one refers to bounds on the number of active constraints at the point under consideration.     

List coloring with requests

Let be a graph with a list assignment . Suppose a preferred color is given for some of the vertices; how many of these preferences can be respected when -coloring ? We explore several natural questions arising in this context, and propose directions for further research.