On the Constructive Algorithm for Stability Analysis of an Equilibrium Point of a Periodic Hamiltonian System with Two Degrees of Freedom in the Second-order Resonance Case

This paper is concerned with a nonautonomous Hamiltonian system with two degrees of freedom whose Hamiltonian is a 2π-periodic function of time and analytic in a neighborhood of an equilibrium point. It is assumed that the system exhibits a secondorder resonance, i. e., the system linearized in a neighborhood of the equilibrium point has a double multiplier equal to ?1. The case of general position is considered when the monodromy matrix is not reduced to diagonal form and the equilibrium point is linearly unstable. In this case, a nonlinear analysis is required to draw conclusions on the stability (or instability) of the equilibrium point in the complete system.In this paper, a constructive algorithm for a rigorous stability analysis of the equilibrium point of the above-mentioned system is presented. This algorithm has been developed on the basis of a method proposed in [1]. The main idea of this method is to construct and normalize a symplectic map generated by the phase flow of a Hamiltonian system.It is shown that the normal form of the Hamiltonian function and the generating function of the corresponding symplectic map contain no third-degree terms. Explicit formulae are obtained which allow one to calculate the coefficients of the normal form of the Hamiltonian in terms of the coefficients of the generating function of a symplectic map.The developed algorithm is applied to solve the problem of stability of resonant rotations of a symmetric satellite.     

两自由度分段线性振动系统的亚谐解

本论文研究了两个自由度分段线性振动系统的亚谐解,其理论结果证明系统可能存在各种类型的亚谐解[(1.31)～(1.34)],如1/2,1/3,1/4,1/5,1/6,…亚谐共振解在模拟计算机的计算结果以及现场实验的结果中得到了部分证实。在一定的系统参数的情况下,模拟计算机的结果有浑沌现象发生。     

Vibrations of Pipes with Internal Flow and Rigid Body Degrees of Freedom

In the present paper the nonlinear dynamics of elastic pipes conveying fluid at arbitrary flow rates are investigated. The nonlinear equations of motion are derived using a unified form of the Lagrange Equations for non-material volumes formulated by Irschik and Holl [1], see also Chapter 3 of [2]. In a first step cantilevered pipes are considered using elastic degrees of freedom combined with a Ritz-Galerkin Ansatz of arbitrary order for modelling the deformations of the pipes. The Lagrange Equations for non-material volumes include a nonzero surface integral of the kinetic energy due to the moving outlet surface at the end of the pipe. The linear equations of motion obtained from this model are then analytically investigated utilizing the corresponding Eigenvalue problem. The results are visualized in an Argand representation of the corresponding Eigenvalues of the system matrix and compared to existing results obtained by using different formulations, such as the Hamilton Principle for Open-Systems, formulated by Benjamin [4], as demonstrated by Païdoussis [5], see also chapter 3.5 of [6]. In a next step an elastic pipe with a rigid body degree of freedom combined with a Ritz-Galerkin Ansatz is modelled with one supported and one free end. The derivation of the equations of motion is performed by using a floating-frame of reference formulation which leads to a system of nonlinear second order differential equations describing the motion of the pipe. Finally, the stability of the solutions of the equations of motion for varying flow rate is studied numerically. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

两自由度非对称三次系统非奇异时的非线性模态及叠加性

本文利用非线性模态子空间的不变性研究两自由度非对称三次系统在非奇异条件下的非线性模态及其模态叠加解有效性，重点考虑这种有效性与模态动力学方程静态分岔之间的关系·大量的数值结果表明，非线性模态解的有效性不仅与其局部性的限制有关，而且与模态动力学方程静态解分岔有关·     

Dynamic Modeling and Force Control of a Redundant Robot for Polishing Applications

For many robotic applications with tasks such as cutting, assembly or polishing, it is necessary to get in contact with the surrounding. In this paper a redundant robot with seven degrees of freedom in a metal polishing task is considered. For simulation as well as for the controller design a dynamic model of the robot and a contact model are required. The equations of motion of the robot are calculated with the Projection Equation in subsystem representation and the contact model contains linear tool elasticities and work piece elasticities. In the case of a polishing task, a constant contact force during the process is required even if the robot moves along a trajectory. Thus some degrees of freedom of the robot tool center point have to be position controlled while the other ones have to be force controlled. The redundant robot offers the possibility to avoid singular positions or to maximize the available end-effector forces within the inverse kinematics and is therefore best suited for polishing large objects. The actual process forces are measured with a six axis force-torque-sensor mounted at the tool center point. These forces are used in a parallel force/position control law to achieve the desired behavior. Results from measurements of a test arrangement are presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

16个和20个自由度的四面体有限元的场函数表达式的显式

本文写出了16个和20个自由度的四面体有限元的场函数表达式的显式.它们是用体积座标L₁,L₂,L₃,L₄来表达的.     

Modeling Nondegenerate Bifurcations of Closures of Solutions for Integrable Systems with Two Degrees of Freedom by Integrable Topological Billiards

It is well known that surgeries of closures of solutions for integrable nondegenerate Hamiltonian systems with two degrees of freedom at a level of constant energy are classified by the so-called 3-atoms. These surgeries correspond to singular leaves of the Liouville foliation of three-dimensional isoenergetic surfaces. In this paper we prove the Fomenko conjecture that all such surgeries are modeled by integrable topological two-dimensional billiards (billiard books).     

泛函积分方程的正解与应用

运用锥拉伸与压缩不动点定理,研究一类泛函积分方程的正解．把所得结果应用于研究常微分方程积分边值问题正解的存在性,所得结果推广和本质上改进了马如云等作者最近的一些结果．     

Using the Elements of Manufacturing Systems Management in the Calculation of the Implementation of a Serial-Modular Industrial Robot within a Flexible Work Cell Designed for Special Applications

In this paper, the authors propose a basic design of a flexible work cell with a parallel organization, destined for the spot welding of AAV carcasses. The cell is serviced by three industrial TTR robots that perform spot welding operations on the carcasses flowing on the conveyor belt to each of the robots performing this operation. This paper presents economic issues on the value of the robots comprised by the system, the calculus of the entire FWC value, the determination of the FWC static configuration, and evaluates the overall profitability of the cell using elements pertaining to the mathematical game theory and the graph theory, as well. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Holling-Ⅲ型食饵捕食系统的四个正周期解

通过使用一般连续理论和微分不等式技巧,研究带有收获项的Holling-Ⅲ型食饵捕食系统的动态特征,并获得带有收获项的Holling-Ⅲ型食饵捕食系统存在四个正周期解的充分条件.     

渐近线性算子方程的四种类型的解

利用拓扑度理论及不动点指数理论,讨论了渐近线性算子方程的四种类型的解(即零解、正解、负解和变号解)的存在性,并将这一抽象结果应用于微分方程两点边值问题.     

Constructive existence and uniqueness for two-point boundary-value problems with a linear gradient term

Constructive existence and uniqueness theorems are established for nonlinear two-point boundary-value problems governed by the equation y″=f(x, y)+p(x)y′, 0?x?1. The existence and uniqueness is established for functions y(x) that satisfy a certain constraint, i.e., that sfncy(x)sfnc is bounded by a known function or that 0?y(x)?M for some M. Applications to scientific problems in the literature are given.     

Solution Space Monodromy of a Special Double Confluent Heun Equation and Its Applications

Theoretical and Mathematical Physics - We consider three linear operators determining automorphisms of the solution space of a special double confluent Heun equation of positive integer order...     

一类泛函微分方程的全局吸引性及应用

采用一种新方法研究时滞泛函微分方程x(t) a(t) (1 x(t) )ln(1 x(t) ) (1 x(t) )F(t,x(·) ) =0 ,的全局吸引性 ,并将所得结果应用于动物体内红血球生长模型 ,得到的全局吸引的充分条件 ,推广和改进了已有的结果     

O.R. Applications in Industry and Problems of Industrialisation of a Developing Economy with Special Reference to India

The paper has two distinct parts. The first part reviews industrial applications of O.R. in developing countries in general and India in particular. Based on the analysis, the paper suggests concrete steps for further use of operational research in industry.The second part of the paper deals critically with the problems of industrialisation leading to a specific industrial structure in the economy of a developing country. Analysing various relevant criteria for industrialisation of developing economies the paper outlines a methodology suitable for modelling the problem. It then attempts to identify the prerequisites for successful use of O.R. in the multicriteria problem of industrialisation. The paper also discusses the role that national and international agencies can play in bringing about more meaningful applications of O.R. in developing economies.