Nonminimal Kane's Equations of Motion for Multibody Dynamical Systems Subject to Nonlinear Nonholonomic Constraints

Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations. Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint equations for a holonomically constrained particle in the gravitational field.     

Dynamic equations in descriptor form

This paper studies a general form of sets of equations that is often the product of problem formulation in large-scale systems, especially when the equations are expressed in terms of the natural describing variables of the system. Such equations represent a broad class of time-evolutionary phenomena, and include as special cases ordinary static equations of arbitrary dimension, ordinary state-space equations, combinations of static and dynamic equations, and noncausal systems. The main thrust of the paper is to show (for sets of linear equations) that familiar concepts of dynamic system theory can be extended to this more general class, although sometimes with significant modification. Two new (and essentially dual) concepts, that of solvable and conditionable sets of equations, are found to be fundamental to the study of equations of this form. The notion of initial conditions, although not directly related to a state, is used as a general solution method for equations of this type. In addition a set of necessary and sufficient conditions for a set of dynamic equations to contain an embedded state-space representation is derived.     

Stopping Criteria for Anisotropic PDEs in Image Processing

A number of nonlinear diffusion-like equations have been proposed for filtering noise, removing blurring and other applications. These equations are usually developed as time independent equations. An artificial time is introduced to change these equations to parabolic type equations which are then marched to a steady state. In practice the time iteration is stopped before the steady state is reached. The time when to stop the iteration is usually determined manually for each case. In this study we develop a more automatic procedure for stopping the time integration.     

Formulation of the State-space Equations for Non-linear Networks

The formulation of state-space equations is discussed for a general class of nonlinear networks, and a block diagram derived summarizing the general non-linear network state-space relationships. Certain special forms of the nonlinear state-space equations are then derived for restricted classes of network; these are the Brayton-Moser equations, the Lagrangian and co-Lagrangian equations and the Hamiltonian equations.     

具有对称循环结构的大系统Riccati方程的求解

本文研究了具有对称循环结构的大系统的代数Ｒｉｃｃａｔｉ方程和Ｌｙａｐｕｎｏｖ矩阵方程的求解问题，结果表明，这类系统的代数Ｒｉｃｃａｔｉ方程和Ｌｙｐａｐｕｎｏｖ矩阵方程的求解问题可以简化为求解Ｎ／２＋１个独立的低阶方程，做为一个应用，这类系统的二次型最优控制问题和鲁棒二次型最优控制问题也可以简化。     

面向对象设计在捷联惯导算法仿真中的应用

针对捷联惯导系统（SINS）的算法设计,介绍了SINS的姿态、速度和位置基本微分方程组;以解捷联惯导一阶微分方程组的算法仿真为例,提出了基于面向对象程序设计中类的概念和运算符重载的功能,设计了捷联惯导算法的四阶龙格-库塔数值解法;该设计为工程实现中直接求解含标量、向量和矩阵等混合形式的一阶微分方程组的数值解提供了一定的参考价值;仿真结果表明：即使对恶劣的纯锥运动,该算法精度也很高。     

粒子群算法在求解方程组中的应用

提出了采用粒子群算法求解线性方程组和非线性方程组的智能算法。采用粒子群算法求解方程组具有形式简单、收敛迅速和容易理解等特点,且能在一次计算中多次发现方程组的解,可以解决非线性方程组多解的求解问题,为线性方程组和非线性方程组的求解提供了一种新的方法。     

Towards algebraic multigrid for elliptic problems of second order

An algebraic multigrid method is developed which can be used as a preconditioner for the solution of linear systems of equations with postitive definite matrices. The method is directed to equations which arise from the discretization of elliptic equations of second order, but only the matrix is the source for the information used by the algorithm. One has only to know whether the matrix stems from a 2-dimensional or 3-dimensional problem and whether the elliptic equations are scalar equations or belong to a system.     

On a class of positive linear differential equations with infinite delay

We give an explicit criterion for positivity of the solution semigroup of linear differential equations with infinite delay and a Perron-Frobenius type theorem for positive equations. Furthermore, a novel criterion for the exponential asymptotic stability of positive equations is presented. Finally, we provide a sufficient condition for the exponential asymptotic stability of positive equations subjected to structured perturbations. A simple example is given to illustrate the obtained results.     

不可压缩流稳定性的多尺度分析与数值模拟

为了研究小尺度不可压缩周期流的稳定性,应用多尺度分析方法获得控制其扰动流的大尺度均场方程。对稳态平行流,根据均场方程得到控制大尺度扰动流稳定性的涡流粘性系数。为了验证多尺度理论预测的正确性,采用可以避免速度场和压力场失耦且具有高精度的时间分裂拟谱算法,对不同参数和初始条件下的均场方程以及原始扰动流控制方程进行了数值求解。     

Robust Finite Volume Schemes for Two-Fluid Plasma Equations

Two-fluid plasma equations are derived by taking moments of Boltzmann equations. Ignoring collisions and viscous terms and assuming local thermodynamic equilibrium we get five moment equations for each species (electrons and ions), known as two-fluid plasma equations. These equations allow different temperatures and velocities for electrons and ions, unlike ideal magnetohydrodynamics equations. In this article, we present robust second order MUSCL schemes for two-fluid plasma equations based on Strang splitting of the flux and source terms. The source is treated both explicitly and implicitly. These schemes are shown to preserve positivity of the pressure and density. In the case of explicit treatment of source term, we derive explicit condition on the time step for it to be positivity preserving. The implicit treatment of the source term is shown to preserve positivity, unconditionally. Numerical experiments are presented to demonstrate the robustness and efficiency of these schemes.     

Numerical solution of nonstationary problems for a system of nernst-planck equations

The mathematical model of electricity and mass transfer is based on the equations for charged particles (ions and cations) in the electrolyte, i.e., the Nernst-Planck equations. These equations are supplemented by the equation for the electric field and the motion equations for the electrolyte as a continuum. The paper mostly focuses on the construction of the time approximation for the approximate solution of nonstationary problems. The system of Nernst-Planck equations is characterized by a quadratic nonlinearity. Special linearization schemes are proposed for taking this into account. Computational algorithms are studied on a model problem for the binary electrolyte (two kinds of charged particles).     

On the modelling of actuator dynamics and the computation of prescribed trajectories

The dynamics of actuator mechanisms is presented using a multibody modelling approach to concisely express the structure of the system equations. The Lagrange equations are used to obtain the Newton–Euler equations to which constraint equations are augmented to form a system of differential algebraic equations. The differential algebraic equations are cast as ordinary differential equations and computed using the numerical integrator LSODAR of Petzold and Hindmarsh. Constraint compliance is investigated to ensure the accuracy of the results. Animation of an excavator and wheel loader system is presented and graphs of constraint forces show the nature of the actuator dynamics involved in maintaining specified bucket trajectories. The model is general in nature and caters for arbitrary mechanism connectivity and physical properties.     

A generalized solution of an initial-boundary value problem arising in the mechanics of discrete-continuous systems

We define a generalized solution of an initial-boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We prove that the problem is well-posed and has a unique generalized solution. An analytical formula for the solution is found. Such systems of differential equations arise in studying discrete-continuum mechanical systems.     

Numerical use of {m,n}-approximation method thermoelastic anisotropic thin shell theory equations represented in a special form

A linear uncoupled quasi-static theory of thermoelastic anisotropic thin shells of constant thickness is formulated. In the derivation of equations and boundary conditions, a variant of the {$m,n$}-approximation method, which is based on the variational principle of the thermoelasticity theory, is used. According to this method, the unknown functions are represented in the form of a series of Legendre polynomials in the transverse coordinate that agree with the force boundary conditions on the facial surfaces. From the system of equations of the constructed theory for generalised displacements, strains, and stresses, a system of equations for generalised displacements is obtained; this system is solved for the second derivatives of generalised displacements with respect to one of the Gaussian parameters of the middle surface. For a system of partial differential equations represented in such a form, the known techniques for the reduction of systems of two-dimensional equations to normal systems of ordinary differential equations, which can be solved by standard numerical methods, can be applied. The system of equations for generalised displacements is reduced to a normal system of ordinary differential equations in the case of a plane deformation of a cylindrical panel. Through the use of these equations and the S. K. Godunov method of orthogonal successive substitutions, the bending problems of a planar beam subjected to a mechanical load or a thermal load and a circular cylindrical panel exposed to a thermal load are numerically solved. It is demonstrated that the proposed equations are particularly suitable for the analysis of boundary effects in planar beams and circular cylindrical panels.     

Boundary value problems for a class of impulsive functional equations

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differential equations with maximum and integro-differential equations. In this paper, we also prove that the Lipschitzian character of the function which introduces the functional dependence in a differential equation is not a necessary condition for the development of the monotone iterative technique to obtain a solution and to approximate the extremal solutions to the equation in a given functional interval. The corresponding results are established for the impulsive case. The general formulation includes several types of functional dependence (delay equations, equations with maxima, integro-differential equations). Finally, we consider the case of functional dependence which is given by nonincreasing and bounded functions.     

Nonlinear generalized equations of motion for multi-link inverted pendulum systems

In this paper, the equations of motion for a general multi-link inverted pendulum system are derived. Assumptions previously employed to simplify such formulation are removed. The pendulum system is more general and includes nonlinear friction terms to suit various engineering applications. The generalized equations are first developed in the absolute coordinate system using Lagrange's technique, then a simple linear transformation is proposed to obtain the set of nonlinear equations in the DevanitHartenberg coordinate system. The equations of motion for double and triple link inverted pendulum systems are given as examples for such dynamics equations.     

在频域中利用同态滤波增强图像对比度

在介绍基于照明反射模型的同态滤波模型原理、实现过程和特点的基础上,在频域内通过对高斯高通滤波器、巴特沃斯高通滤波器、指数高通滤波器的改进后得出三种同态滤波器,并对三种同态滤波器通过实验结果给出适用的滤波模型和表达式参数。由对同一幅照明不良会使图像亮度不足和细节模糊,而且图像信噪比很低,图像对比度明显变差的图像处理结果表明,巴特沃斯同态滤波函数优于其它两种同态滤波函数,对光照不足的图像进行灰度动态范围压缩和对比度增强效果显著。     

Counting equations in algebraic attacks on block ciphers

This paper is about counting linearly independent equations for so-called algebraic attacks on block ciphers. The basic idea behind many of these approaches, e.g., XL, is to generate a large set of equations from an initial set of equations by multiplication of existing equations by the variables in the system. One of the most difficult tasks is to determine the exact number of linearly independent equations one obtain in the attacks. In this paper, it is shown that by splitting the equations defined over a block cipher (an SP-network) into two sets, one can determine the exact number of linearly independent equations which can be generated in algebraic attacks within each of these sets of a certain degree. While this does not give us a direct formula for the success of algebraic attacks on block ciphers, it gives some interesting bounds on the number of equations one can obtain from a given block cipher. Our results are applied to the AES and to a variant of the AES, and the exact numbers of linearly independent equations in the two sets that one can generate by multiplication of an initial set of equations are given. Our results also indicate, in a novel way, that the AES is not vulnerable to the algebraic attacks as defined here.