用线性插值法求单摆运动周期的近似解

利用线性插值的方法,提出了一个任意摆角条件下的单摆运动周期的近似公式.并利用Mathematica软件将该公式与精确解进行了比较,还与其他近似公式进行了对比.结果表明,该公式的近似程度相当好.     

平方律阻力下抛射体运动的一种解法

本文求出了平方律阻力下运动的抛射体,以斜率 f′为参数的非线性微分方程解的积分表示式,讨论了其物理意义,还得到射程的近似解析表达式.     

三线摆的运动方程、周期及角位置概率分布

基于保守系统拉格朗日方程给出三线摆在大摆角运动时的微分方程,以及小摆角线性振动近似处理方法,在考虑三线摆的结构尺寸取相应近似条件下,讨论了三线摆在大摆角和小摆角两种不同情况下的运动微分方程、周期及角位置概率密度分布情况及其在实验中的应用.     

滑移爆轰作用下飞板运动的解析解

 给出了滑移爆轰作用下飞板运动的近似解析解,应用其结果计算炸药滑移爆轰时飞板的运动,同实验结果和二维数值模拟计算结果吻合,表明该近似解析解具有较高的精度。解析解简洁,便于工程应用。     

精确计算非旋波近似下二能级系统的能谱和动力学性质

利用相干态正交化展开法,精确求解了非旋波近似下Jaynes-Cummings模型的能谱和动力学性质.与近似下解析解比较发现,在弱耦合和强耦合区近似解析解与数值精确解符合很好,但在中间耦合区符合较差. 关键词： 相干态正交化展开 非旋波近似 Jaynes-Cummings模型     

环形浅液池内热毛细对流的渐近解

为了了解微重力下水平温度梯度作用时环形浅液池内的热毛细对流特征,采用渐近线方法求得了环形浅液池内热毛细对流的近似解析解,得到了主流区速度场和温度场的表达式,并与数值模拟结果进行了比较,两者基本吻合.     

倒置摆的运动研究

构建一种倒置摆模型,运用理论分析与MATLAB数值计算相结合的方法给出倒置摆做小角度运动时的近似解.结果表明:存在一个临界频率,当驱动频率小于临界频率时,倒置摆会落下;当驱动频率大于临界频率时,倒置摆可以不下落.     

利用线化和校正法求非线性单摆运动的周期

应用线化和校正方法,研究了单摆的非线性振动,作出了周期比和相对误差随摆角的变化曲线.将所得近似解与精确解比较可知,该方法具有简单实用,精度高,相对误差低等优点,对于求解非线性振动问题具有一定的实用价值.     

大摆角耦合摆的运动规律的数值分析

基于并联耦合摆理论模型,利用数值方 法研究了在较大摆角情况下并联耦合摆的运动规律. 通过分析该系统在较大摆角时摆球的相轨迹图像和庞 加莱截面图像, 可发现并联耦合摆在较大摆角下的运 动是准周期运动, 该规律与摆球质量是否相同无关     

考虑空气阻力的抛体射程

空气阻力对抛体的运动可以产生显著的影响.运用近似的方法处理超越方程,给出了考虑空气阻力的抛体运动落地时间和射程与抛射角的近似解析关系,并且与数值解进行了比较.     

刚体定点转动的张量描述

通过引入转动张量来描述刚体的定点转动,避免了在用角位移描述刚体定点转动时所遇到的问题,即角位移在它是有限大小和无限小时属性发生了变化.验证了对于刚体定点无限小转动,可以分别采用角位移矢量和转动张量描述,两者是等价的.     

Analytical solutions to the electromagnetic field in a cylindrical shell excited by external axial current

The solutions to the electromagnetic field excited by a long axial current outside a conductive and magnetic cylindrical shell of finite length are studied in this paper. The more accurate analytical solutions are obtained by solving the proper boundary value problems by the separation variable method. Then the solutions are simplified according to asymptotic formulas of Bessel functions. Compared with the accurate solutions, the simplified solutions do not contain the Bessel functions and the inverse operation of the singular matrix, and can be calculated out fast by computers. The simplified solutions are more suitable for the cylindrical shell of high permeability and conductivity excited by a high frequency source. Both of the numerical results and the physical experimental results validate the simplified solutions obtained.     

MHD Boundary Layer Flow of a Non-Newtonian Fluid on a Moving Surface with a Power-Law Velocity

A theoretical analysis for MHD boundary layer flow on a moving surface with the power-law velocity is presented. An accurate expression of the skin friction coefficient is derived. The analytical approximate solution is obtained by means of Adomian decomposition methods. The reliability and efficiency of the approximate solutions are verified by numerical ones in the literature.     

Arbitrary <Emphasis Type="Italic">l</Emphasis>-state solutions of the Schrödinger equation for the Eckart potential with an improved approximation of the centrifugal term

Applying an improved approximation scheme to the centrifugal term, the approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented. Bound state energy eigenvalues and the corresponding eigenfunctions are obtained in closed forms for the arbitrary radial and angular momentum quantum numbers, and different values of the screening parameter. The results are compared with those obtained by the other approximate and numerical methods. It is shown that the present method is systematic, more efficient and accurate.     

An accurate and robust numerical method for micromagnetics simulations

We propose a new robust, accurate, and fast numerical method for solving the Landau–Lifshitz equation which describes the relaxation process of the magnetization distribution in ferromagnetic material. The proposed numerical method is second-order accurate in both space and time. The approach uses the nonlinear multigrid method for handling the nonlinearities at each time step. We perform numerical experiments to show the efficiency and accuracy of the new algorithm on two- and three-dimensional space. The numerical results show excellent agreements with exact analytical solutions, the second-order accuracy in both space and time, and the energy conservation or dissipation property.     

完整力学系统的高阶运动微分方程

从质点系的牛顿动力学方程出发,引入系统的高阶速度能量,导出完整力学系统的高阶Lagrange方程、高阶Nielsen方程以及高阶Appell方程,并证明了完整系统三种形式的高阶运动微分方程是等价的.结果表明,完整系统高阶运动微分方程揭示了系统运动状态的改变与力的各阶变化率之间的联系,这是牛顿动力学方程以及传统分析力学方程不能直接反映的.因此,完整系统高阶运动微分方程是对牛顿动力学方程及传统Lagrange方程、Nielsen方程、Appell方程等二阶运动微分方程的进一步补充. 关键词： 高阶速度能量 高阶Lagrange方程 高阶 Nielsen方程 高阶Appell方程     

Simulating non-linear coupled oscillators by an iterative differential quadrature method

An iterative method based on differential quadrature rules is proposed as a new unified frame of resolution for non-linear two-degree-of-freedom systems. Dynamical systems with Duffing-type non-linearity have been considered. Differential quadrature rules have been applied with a careful distribution of sampling points to reduce the governing equation of motion to two second-order non-linear, non-autonomous ordinary differential equations and to solve the time-domain problem. The time domain of the problem is discretized by means of time intervals, with the same distribution of sampling points used to discretize the space domain (which can be seen as a single interval). It will be shown that accurate solutions depend not only on the choice of the distribution of sampling points, but also on the length of the time interval one refers to in the computations. The numerical results, utilized to draw Poincaré maps, are successfully compared with those obtained using the Runge-Kutta method.     

Generalized analytical solutions for secure transmission of signals using a simple communication scheme with numerical and experimental confirmation

A novel explicit analytical solution is reported for the transmission and recovery of information signals using a simple communication scheme. Analytical solutions are obtained for the normalized state equations of coupled second-order chaotic transmitter and receiver systems embedding the information signal. The analytical solution of the difference system obtained from the state equations of the transmitter and receiver systems has been identified as a measure of the recovered information signal which is transmitted securely by chaotic masking. The analytical solutions are used to reveal the nature of synchronization and the enhancement of the amplitude of recovered information signal. The difference signal of the coupled state variables indicating the recovered information signal obtained through numerical simulations is presented to validate the analytical results. The electronic circuit experimental results are presented to confirm the analytical and numerical results of the communication scheme discussed.     

Approximate Analytical Solutions of Dirac Equation with Spin and Pseudo Spin Symmetries for the Diatomic Molecular Potentials Plus a Tensor Term with Any Angular Momentum

Approximate analytical solutions of the Dirac equation are obtained for some diatomic molecular potentials plus a tensor interaction with spin and pseudospin symmetries with any angular momentum. We find the energy eigenvalue equations in the closed form and the spinor wave functions by using an algebraic method. We also perform numerical calculations for the Pöschl-Teller potential to show the effect of the tensor interaction. Our results are consistent with ones obtained before.     

Liquid film and gas flow motion in a microchannel with evaporation

The problem of stabilized combined motion of the gas flow and liquid film in a microchannel under the action of local heating with consideration of evaporation processes was set in selected variables. The exact solutions to the linearized problem were derived. The analytical formulas for calculation of the film thickness stabilized below the heater and the total rate of liquid evaporation were obtained. The technique of approximate calculation of total heat transfer is shown. Exemplary calculations are presented.