应用数学和力学

1995 Vol. 16, No. 9

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Notes on a Study of Vector Bundle Dynamical Systems(Ⅰ)

Liao Shantao

1995, 16(9): 757-766.

Abstract(2087) PDF(542)

Abstract:
This paper is a continuation of a previous one. We still emphasize the discussionon the relation between the dynamics on the base space of a rector bundle and that oneach associated bundle of frames.

General Second Order Fluid Flow in a Pipe

He Guangyu, Huang Junqi, Liu Ciqun

1995, 16(9): 767-773.

Abstract(2453) PDF(797)

Abstract:
It is more satisfactory for fluid materials between viscous and elastic to introducethe fractional calculus approach into the constitutive relationship. This paper employsthe fractional calculus approach to study second fluid flow in a paper. First, we derivethe analytical solution which the derivate order is half and then with the analytical solution we verify the reliability of Laplace numerical inversion based on Crumpalgouithm for the problem, and finally we analyze the characteristics of second order fluid flow in a pipe by using Crump method. The results indicate that the more obviousthe viscoelastic properties of fluid is, the more sensitive the dependence of velocity andstress on fractional derivative order is.

An Example of PDE with Two Attractors

Wang Guanxiang, Xu Zhengyuan, Liu Zengrong

1995, 16(9): 775-780.

Abstract(1772) PDF(560)

Abstract:
A system of reaction-diffusion equations with two attractors is given in this paper.The construction of the attractors is discussed.

Kane’s Equations for Precussion Motion of Variable Mass Nonholonomic Mechanical Systems

Zhang Yueliang, Qiao Yongfen

1995, 16(9): 781-790.

Abstract(1849) PDF(428)

Abstract:
In this paper,the Kane's equations for the Routh's form of variable massnonholonomic systems are established.and the Kane's equations for percussion motionof variable mass holonomic and nonholonomic systems are deduced from them. Secondly,the equivalence to Lagrange's equations for percussion motion and Kane'sequations is obtained,and the application of the new equation is illustrated by an example.

The Adaptive Parameter Incremental Method for The Analysis of Snapping Prohlem

Zhao Qi, Ye Tianqi

1995, 16(9): 791-797.

Abstract(1570) PDF(451)

Abstract:
By the improvement of Riks' and Crisfield's arc-length method,the adaptive parameter incremental method is preasted for predicting the snapping response of structures. Its justification is fulfilled. Finally,the effectiveness of this method is demonstrated by solving the snapping response of spherical caps subjected to centrally distributed pressures.

1995, 16(9): 799-813.

Abstract(1785) PDF(607)

Abstract:

Exponential Attractors for a Generalized Ginzburg-Landau Equation

Gao Hongjun

1995, 16(9): 815-820.

Abstract(1834) PDF(507)

Abstract:
Based on the paper 1, we obtain the existence of exponential attractors for a generalized Ginzburg-Landau equation in one dimension.

Integrable Types of Nonlinear Ordinary DifferentialEquation Sets of Higher 0rders

Tang Guangsong, Yuan Cunde

1995, 16(9): 821-828.

Abstract(2382) PDF(639)

Abstract:
Because of the extensive applications of nonlinear ordinary differential equation in physics,mechanics and cybernetics,there have been many papers on the exact solution to differential equation in some major publications both at home and abroad in recent years Based on these papers and in virtue of Leibniz formula,and transformation set technique,this paper puts forth the solution to nonlinear ordinary differential equation set of higher-orders, moveover,its integrability is proven.The results obtained are the generalization of those in the references.

Studying the Focal Value of Ordinary Differential Equations by Normal Form Theory

Zhang Qichang, A. Y. T. Leung

1995, 16(9): 829-838.

Abstract(2389) PDF(532)

Abstract:
We present a new method to calculate the focal value of ordinary differential equation by applying the theorem defined the relationship between the normal form and focal value,with the help of a symbolic computation language MATHE-MATICA,and extending the matrix representation method.This method can be used to calculate the focal value of any high order terms.This method has been verified by an example.The advantage of this method is simple and more readily applicable.the result is directly obtained by substitution.

Yu Huidan, Zhang Jiefang

1995, 16(9): 839-842.

Abstract(2244) PDF(507)

Abstract:
In this paper two types of similarity reductions of the super KdV equation aregiven by the direct method.

Yuan Yiwu

1995, 16(9): 843-850.

Abstract(2139) PDF(521)

Abstract:
In ref.[1],the wave solutions of nonlinear heat conduction equation are studied. In it, the similar variable ξ is wave variable and it is assumed that the heat conduction coefficient is only the function of the similar variable ξ.In this paper the author forsakes the above-mentioned restraints and studies the similar solutions of the nonlinear conduction equation from the more general angles.