自行车稳定性问题的研究与诠释

根据刚体转动的力矩平衡, 从转动相对定点悬空的角度, 给出自行车“ 转弯不倒”的约束关系, 并由此 剖析自行车在微小扰动情况下, 能够自动恢复稳定的原因. 最后, 结合自行车转弯过程中的转动惯量及回转半径, 给出自行车在“ 转弯不倒”条件下的最大角速度解析式     

基于消失点约束的多相机标定方法

针对多摄像机一维标定算法精度低、抗噪性和稳定性差等问题,提出了基于消失点之间互相约束的多摄像机标定方法.为了避免径向畸变对成像造成的影响,利用欧式空间位置约束的几何特性,进行畸变参数的求取.通过靶标特征点约束结合摄像机的射影不变性排除杂点的干扰,再利用空间消失点之间夹角一致性,以及靶标特征点所构成的直线和消失点的反向射线平行性来求解摄像机的参数.当一维靶标任意运动时,存在着无法区分靶标特征点对应的成像点临界问题,采取反推理论数学分析法可事先避免该问题的出现.通过构建多摄像机系统进行标定实验,可以看出该方法具有较高的标定精度,且随着噪声的增加,标定结果具有一定的抗噪性和稳定性;由相对误差值可知,该方法可应用于多摄像机系统.     

双流体等离子体模型的动力学可容变分

动力学可容变分方法是一种广义哈密顿系统中的李扰动变换方法,能自动保证卡西米尔函数在相应阶数上的守恒性质.通过动力学可容方法得到了双流体在欧拉描述中的一组约束变分,而后利用这组变分对双流体哈密顿量取极值得到了平衡方程.     

随机Duffing单边约束系统的倍周期分岔

通过引进平均约束面和平均跃变方程对随机约束系统的约束条件进行处理，把研究随机光滑系统倍周期分岔的Chebyshev多项式逼近的方法运用到随机非光滑系统中，数值研究表明随机Duffing单边约束系统同样存在丰富的倍周期分岔现象，Chebyshev多项式逼近是研究带有约束的随机非光滑动力系统的有效方法. 关键词： 非光滑动力系统 随机Duffing系统 Chebyshev多项式 倍周期分岔     

高温超导磁约束等离子体推进器杜瓦系统的应力和应变分析

高温超导磁约束等离子体推进器利用磁场的作用,将高温等离子体的能量转化为推进器的推力,对于杜瓦系统的结构有着较高的要求.文中主要介绍了杜瓦系统的基本结构,并利用ANSYS软件分析了杜瓦系统的应力和应变,说明了高温超导磁约束等离子体推进器杜瓦系统的设计满足应力及应变要求.     

相关于弦论的规范不变自对偶场的Faddeev-Jackiw量子化

用Faddeev-Jackiw(FJ)方法对与规范场偶合的规范自对偶场进行了研究, 获得了一个新的辛Lagrangian密度, 导出了此系统的FJ广义括号, 并对其进行了FJ量子化. 进而把FJ方法和Dirac方法进行了比较, 发现在对此系统的量子化中, 两种方法所给出的量子化结果完全是等价的. 通过分析可知FJ方法比Dirac方法要简单, 因FJ方法不需要区分初级约束与次级约束, 而且也不需要区分第一类约束和第二类约束. 故与Dirac方法相比, FJ方法是一种计算上更为经济和有效的量子化方法.     

超对称电动力学系统的Faddeev-Senjanovic量子化

用Faddeev-Senjanovic量子化方法对超对称电动力学系统在一般情况下进行了量子化, 得到了格林函数的生成泛函. 通过对一些约束作线性组合获得了另一个第一类约束, 构造出了该体系的规范生成元, 导出了该系统的规范不变的对称变. 由一个规范条件的自恰性导出了另一个规范条件, 发现超对称电动力学系统的次级第一类约束对应物理电荷守恒律, 从而使过去要算很多次级约束才能截断的约束自然截断, 因而使超对称电动力学系统在一般情况下的Faddeev-Senjanovic量子化被简化.     

论微分约束系统的d-δ对易关系

利用Frobenius可积性定理,研究微分约束系统一个重要的变分法问题：微分运算与变分运算的对易关系. 文中以微分约束的Frobenius可积性理论为依据,在分析线性稳定微分约束系统和仿射微分约束系统的d-δ对易关系基础上,简要论证了微分与变分的非对易子与微分约束的非完整性之间的关系. 对非线性微分约束系统的微分与变分运算的对易关系作了讨论. 给出了三个实例来验证结论. 关键词： 非完整约束 Frobenius可积性 d-δ对易关系     

双边约束条件下随机van der Pol系统的分岔研究

利用随机光滑动力系统的Chebyshev正交多项式逼近方法,研究了双边约束条件下随机van der Pol系统的分岔现象.数值研究表明,双边约束随机van der Pol系统中不仅存在着丰富的倍周期分岔现象,还存在非光滑系统中所特有的擦边分岔.着重研究了随机非光滑系统中的擦边分岔,分析了随机因素对非光滑动力系统中擦边分岔的影响.研究表明,Chebyshev多项式逼近也是研究随机非光滑系统动力学行为的一种有效方法. 关键词： 非光滑动力系统 随机 van der Pol系统 擦边分岔 双边约束     

约束系统量子化中Dirac方法与Faddeev-Jackiw方法的等价性

对约束系统量子化中Dirac方法和 Faddeev-Jackiw方法进行了讨论，并对它们的运动方程、正则量子化的等价性进行证明.找出了两种方法中约束的对应关系. 关键词： Faddeev-Jackiw方法 Dirac方法 约束系统 正则量子化     

基于近似熵测度的自适应随机共振研究

变步长随机共振算法有效解决了绝热近似大参数条件下的弱信号检测问题.基于信号近似熵测度的自适应随机共振，实现了变步长随机共振最优输出的自适应求解.周期信号的近似熵不受其幅值和相位变化的影响，而只与其频率及信噪比有关.因此，按照原始数据的采样条件，构造待检测频率在预定信噪比下的标准信号，并以其近似熵为基准，通过自动调节非线性系统的结构参数和计算步长，求得系统输出的近似熵距离矩阵.该矩阵中的最小值所对应的即为自适应条件下非线性动力系统的最优参数.     

A QUANTUM MECHANICAL DESCRIPTION FOR QUASI-LANDAU RESONANCES I:FORMULATION AND GENERAL PROPERTIES

The problem of a hydrogen atom in a strong magnetic field is solved quantum-mechanically in the (r,ρ,φ) coordinate system.The main part of the Hamillonian can be solved by separation variables and the remaining part is small and is treated as a perturbation,The zeroth order energy and wave function are obtained, the expression for the first perturbation energy is derived, the well-known quasi-Landau resonance interval 3/2h ω_C near thresold and the approximate scaling law ³γ≈1 are dediced amd the approximate dynamical symmetry possessed by this system is found.     

Potential method of integration for solving the equations of mechanical systems

This paper is intended to apply a potential method of integration to solving the equations of holonomic and nonholonomic systems. For a holonomic system, the differential equations of motion can be written as a system of differential equations of first order and its fundamental partial differential equation is solved by using the potential method of integration. For a nonholonomic system, the equations of the corresponding holonomic system are solved by using the method and then the restriction of the nonholonomic constraints on the initial conditions of motion is added.     

Analysis of skew plate problems with various constraints

This paper presents the application of the modified Rayleigh-Ritz method with Lagrange multipliers to analyze skew plate problems with various constraints. By this procedure one can satisfy both geometric and natural boundary conditions of skew plates. To demonstrate the accuracy and versatility of the method, several examples of bending, vibration and buckling of skew plates are solved, and results are compared with those obtained by other approximate methods.     

Tau method approximation for radiative transfer problems in a slab medium

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.     

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.     

Integrable models of black holes and their generalizations in the theories of supergravity and superstrings

A new class of integrable models of (0+1)-and (1+1)-dimensional dilaton gravity coupled to any number of scalar fields is introduced and briefly discussed. These models can be reduced to a system of Liouville equations that are coupled through energy and momentum constraints. The constraints can be explicitly solved, thus giving an explicit analytic solution of the theory. In particular, these integrable models describe spherically symmetric black holes and branes of supergravity theories in higher dimensions.     

Free vibrations of a mono-coupled periodic system

Vibration problems of periodic systems can be analyzed efficiently by means of the transfer matrix method. The frequency equation for the whole system is shown to be obtained in terms of the eigenvalues, or their natural logarithms, which are often called “propagation constants”, of the transfer matrix for a single periodic subsystem. In case of a mono-coupled system this frequency equation may be solved graphically by using the propagation constant curve, thereby saving a great deal of computational effort. Two types of mono-coupled systems are considered as numerical examples: a spring-mass oscillating system and a continuous Timoshenko beam resting on regularly spaced knife-edge supports. Depending on whether the transfer matrix is derived by an analytical procedure or by the finite element method, the numerical solutions become either exact or approximate.     

一种全球定位系统接收机单点定位的新算法及数值试验

借助于Bancroft方法快速决定全球定位系统中接收机的大概位置，可作为观测方程线性化的初值.采用最小二乘法来求解方程时，观测数据存在较大误差(即出现粗差)的情况下，最小二乘解会出现不稳定性，即问题呈不适定性.为了克服解的不适定性，引入了正则化方法，采用正则化方法及正则化参数最优选择来提高抗粗差能力.实验结果表明，利用这种定位方法的抗粗差能力有一定的改进，这对实时、快速定位有重要意义. 关键词： 全球定位系统 Bancroft方法 最小二乘法 正则化