共查询到20条相似文献,搜索用时 31 毫秒
1.
IntroductionHamiltoniansystemsareveryimportantinmathematics,physicsandmechanics.SpeciallyafterFengKang[1]firstproposedthesymplecticnumericalmethodforfinitedimensionalHamiltoniansystemin 1 980s,thestudyofHamiltoniansystemhasbeenfurtherimprovedinboththeoryandapplication .ItisthereforenaturaltoconsidertheproblemaboutwhichkindofpartialdifferentialequationscanberewrittenorrepresentedbyHamiltoniansystem .SuchkindofproblemhasnowbeenwarmlystudiedbymanymathematiciansandphysicianssuchasinRefs.[2 -5] … 相似文献
2.
贺天兰 《应用数学和力学(英文版)》2001,22(9):1096-1104
IntroductionInrecentyears,thestudyofintegrabilityofdiscretenonlineardynamicalsystemsgovernedbyadifferenceequation (ormaps)hasbecomethefocusofinterestandanactivedomainofresearchbyalotofappliedmathematiciansandmechanicians.Socalledintegrabilityofatwo_dim… 相似文献
3.
In this paper, problems of bending of a thin plate under the action of in-plane forces are studied by using the method of multiple scales. 相似文献
4.
5.
6.
Projected Runge-Kutta (R-K) methods for constrained Hamiltonian systems are proposed. Dynamic equations of the systems, which are index-3 differential-algebraic equations (DAEs) in the Heisenberg form, are established under the framework of Lagrangian multipliers. R-K methods combined with the technique of projections are then used to solve the DAEs. The basic idea of projections is to eliminate the constraint violations at the position, velocity, and acceleration levels, and to preserve the total energy of constrained Hamiltonian systems by correcting variables of the position, velocity, acceleration, and energy. Numerical results confirm the validity and show the high precision of the proposed method in preserving three levels of constraints and total energy compared with results reported in the literature. 相似文献
7.
In this paper, finite subharmonic bifurcations have been discussed by means of some examples. It is found that for centrally
symmetric system, under small disturbance, if it has two independant sequences of subharmonic bifurcations, the system passes
to chaos (horeseshoe) through finite subharmonic bifurcations, and that for noncentrally symmetric system, the relation between
subharmonic bifurcations and horseshoe is complicated. 相似文献
8.
Alberto Baider Richard C. Churchill David L. Rod 《Journal of Dynamics and Differential Equations》1990,2(4):451-481
This paper investigates the monodromy representation of the normal variational equation along a phase curve of a two-dimensional complex analytic Hamiltonian system. Geometrical conditions are presented which guarantee reducibility, together with additional hypotheses to ensure complete reducibility. Symmetries in the equations are treated in detail. Applications to establishing the nonintegrability of specific systems are presented. 相似文献
9.
10.
Eugeniusz Zieniuk Agnieszka Boltuc 《International Journal of Solids and Structures》2006,43(25-26):7939-7958
The paper presents a non-element method of solving boundary problems defined on polygonal domains modeled by corner points. To solve these problems a parametric integral equation system (PIES) is used. The system is characterized by a separation of the approximation of boundary geometry from the approximation of boundary functions. This feature makes it possible to effectively investigate the convergence of the obtained solutions with no need of performing the approximation of boundary geometry. The testing examples included confirm high accuracy of the solutions. 相似文献
11.
Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under
parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the
system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation
with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary
order. An example is studied in detail and some numerical results are given to illustrate the above procedure.
The project supported by the Post-Doctoral Foundation of China 相似文献
12.
Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructi... 相似文献
13.
将列车桥梁(轨道)视为整体系统,列出轮轨衔接条件,运用弹性系统动力学总势能不变值原理和形成系统矩阵的“对号入座”法则,建立车桥(轨)系统振动方程,从而得到车桥(轨)系统振动方程的适定解。 相似文献
14.
I.IntroductionThemethodofseparationofvariablesisimportanttosolvethesoluti0n0fprobIem0fmathematicalphysics,butmanyproblen1sofmathematicalphysicscannotseparatet'ariab1es,thereforeitrestrictstheranget0appIicatemethodofseparationofvariable.Inthepaperlll,Zhong… 相似文献
15.
Hua-Jiang Ouyang 《Acta Mechanica Solida Sinica》1993,6(4):453-458
The general expression of Hamiltonian partial differential equation for 3-D anisotropic elasticity is derived in this paper. It is a two-variable mixed formulation based on which new analytic and semi-analytic methods can be introduced. 相似文献
16.
刘长泰 《应用数学和力学(英文版)》1985,6(5):473-482
On the basis of a certain theory if we can predict the composition of a specified material in engineering and we can successfully produce the very material instantly according to the theoretical results, this is what the engineering hopes in the practical application. For fulfilling this purpose, the auther had to investigate an appropriate theory and chose few materials to make composites, so that enabling the produced composite materials to be in good agreement with the object material given beforehand. In this paper the theory is presented in the three proceeding parts and the results are given in the fourth part. Theoretical calculations were worked out for the composites of the two object materials given in engineering. Composites were produced according to the computational resultes. Experiments were made and their results were satisfactory.The N. W. Institute of Nuclear Technology 相似文献
17.
The eigenvalue problem of the Hamiltonian operator associated with plane elasticity problems is investigated.The eigenfunctions of the operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region.The completeness of the eigenfunctions is then proved,providing the feasibility of using separation of variables to solve the problems.A general solution is obtained with the symplectic eigenfunction expansion theorem. 相似文献
18.
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators. 相似文献
19.
潘秀德 《应用数学和力学(英文版)》1988,9(3):311-316
In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that
the combined KdV equation can be reduced to the Painlevé equation. Furthermore, utilizing special transformations of similarity
variables, we derive a kind of new partial differential equations. 相似文献