变质量非完整力学系统的非等时变分方程和积分不变量

给出变质量非完整力学系统的非等时变分方程,研究它们的解,并证明在一定条件下可利用第一积分来得到非等时变分方程的特解,最后利用正则方程和变分方程证明,可由第一积分直接构造系统的积分不变量.     

基于微分变分原理研究相空间中非完整系统的守恒律

为了进一步寻求动力学系统的守恒律,文章基于微分变分原理研究相空间中非完整力学系统的守恒律.首先从非保守系统的Hamilton原理出发,建立了相空间中非完整非保守系统的微分变分原理;其次,通过引进广义变分,给出了此微分变分原理在无限小变换下的不变性条件;最后,导出了相空间中非完整非保守力学系统的守恒律.文末举例说明结果的应用.     

小扰动对力学系统极值性和对称性的影响

完整保守的和非完整非保守的力学系统在受到小干扰力作用的情况下，系统在无干扰时的变分泛函的驻值性与其Ｎｏｅｔｈｅｒ对称性会发生变化．在本文中，我们研究小干扰力作用不改变力学系统原有的极值性和对称性的条件，并给出了几种常见情形下的结果．     

完整力学系统运动方程的代数结构

本文研究完整力学系统运动方程的代数结构．证明，一切完整力学系统的运动方程都具有相容代数结构，并且具有Ｌｉｅ容许代数结构．证明，特殊完整力学系统不仅具有Ｌｉｅ容许代数结构，而且具有Ｌｉｅ代数结构．     

关于力学系统的对称性

力学系统有各种对称性。该文就完整力学系统举例说明各种对称性之间的关系。     

LRC电路系统的对称性与守恒量

Lagrange力学在类力学系统中有着重要的应用,利用Lagrange方程,可用来处理一些类力学系统的问题.本文运用Lagrange方程处理LRC电路系统,通过引入群的无限小变换,可以获得该类力学系统的对称性和守恒量.     

特殊非完整力学系统的 Lagrange 对称性与守恒量

研究特殊非完整力学系统的Lagrange对称性,给出特殊非完整力学系统的Lagrange对称性的定义和判据,并得到特殊非完整力学系统的Lagrange对称性导致守恒量（第一积分）的条件和形式。通过算例说明结果的应用。     

力学模型在磁学中的应用一例

本文所介绍的力学系统与铁磁材料在外磁场中的行为十分相似,即二者的相图十分相似;力学系统的势能类似于铁磁材料的自由能．     

非完整力学系统相对于非惯性系的Hamilton原理

<正> 非完整力学系统的许多运动微分方程已被推广到非惯性系。这种推广既具有理论意义,也具有实际价值。本文把力学系统的Hamilton原理推广到非惯性系,给出非完整力学系统相对于非惯性系的Holder形式和CycлoB形式的Hamilton原理,并举例说明其应用。 一、力学系统相对于非惯性系的一般形式的 Hamilton原理 研究质量为m_i(i=1,2,,…,n)的n个质点组成的力学系统相对于非惯性系ox′y′z′的运动,设非惯性系ox′y′z′与大质量刚体固连在一起,其相对于某惯性系的平动加速度a_0,角速度     

非惯性系中单面约束系统的微分变分原理

研究非惯性系中单面约束力学系统的微分变分原理。得到了具有单面完整和单面Chetaev型非完整约束的力学系统的D’Alembert原理、Jourdain原理和Gauss原理。给出了非惯性系中单面约束系统带乘子形式的各类运动方程。     

一类离散时滞随机系统的稳定性分析

针对一类不确定随机离散变时滞系统,建立了随机稳定性标准,该系统中随机干扰满足布朗运动。选取合适的李雅普诺夫函数,借助于随机稳定性理论、自由权矩阵和线性矩阵不等式等方法,给出并证明了使得该系统随机稳定的充分条件,所有结果以线性矩阵不等式的形式给出,应用例子和仿真表明所给稳定性标准的有效性。     

可控随机非完整Hamilton系统的矩稳定

研究了可控随机非完整Hamilton系统的矩稳定性的条件，通过恰当地选择控制参量u，从而使系统满足稳定性条件，首先，给出可控随机非完整Hamilton系统的运动方程和平衡方程，然后，讨论了可控随机非完整Hamilton系统的均值稳定性的条件。     

On the stochastic dynamics of molecular conformation

An important functioning mechanism of biological macromolecules is the transition between different conformed states due to thermal fluctuation. In the present paper,a biological macromolecule is modeled as two strands with side chains facing each other,and its stochastic dynamics including the statistics of stationary motion and the statistics of conformational transition is studied by using the stochastic averaging method for quasi Hamiltonian systems. The theoretical results are confirmed with the results from Monte Carlo simulation.     

100 years of Einstein’s theory of Brownian motion: from Pollen grains to protein trains—1

Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years Brownian motion has not only revolutionized our fundamental understanding of the nature ofthermal fluctuations in physical systems, but it has also explained many counterintuitive phenomena in earth and environmental sciences as well as in life sciences. This 2-part article begins with a brief historical survey and an introduction to the concepts and theoretical techniques for studying Brownian motion. Then, in Part 2 a discussion on rotational Brownian motion and Brownian shape fluctuations of soft materials is followed by an elementary introduction to two of the hottest topics in this contemporary area of interdisciplinary research, namely,stochastic resonance andBrownian ratchet.     

Fluctuation Theorems of Work and Entropy in Hamiltonian Systems

Fluctuation theorems are a group of exact relations that remain valid irrespective of how far the system has been driven away from equilibrium. Other than having practical applications, like determination of equilibrium free energy change from nonequilibrium processes, they help in our understanding of the second law and the emergence of irreversibility from time-reversible equations of motion at microscopic level. A vast number of such theorems have been proposed in literature, ranging from Hamiltonian to stochastic systems, from systems in steady state to those in transient regime, and for both open and closed quantum systems. In this article, we discuss about a few such relations, when the system evolves under Hamiltonian dynamics.     

A minimax optimal control strategy for uncertain quasi-Hamiltonian systems

A minimax optimal control strategy for quasi-Hamiltonian systems with bounded parametric and/or external disturbances is proposed based on the stochastic averaging method and stochastic differential game. To conduct the system energy control, the partially averaged Ito stochastic differential equations for the energy processes are first derived by using the stochastic averaging method for quasi-Hamiltonian systems. Combining the above equations with an appropriate performance index, the proposed strategy is searching for an optimal worst-case controller by solving a stochastic differential game problem. The worst-case disturbances and the optimal controls are obtained by solving a Hamilton-Jacobi-Isaacs （HJI） equation. Numerical results for a controlled and stochastically excited DulTlng oscillator with uncertain disturbances exhibit the efficacy of the proposed control strategy.     

中立型随机线性随机大系统的稳定性

讨论了时滞中立型线性随机系统的平凡解的几乎渐近稳定性,建立了确定时滞中立型线性随机系统解的极限集位置的充分条件,并应用到时滞中立型线性随机大系统的几乎渐近稳定性的分析中,得到了大系统渐近稳定的代数判据.     

Nonlinear stochastic optimal bounded control of hysteretic systems with actuator saturation

A modified nonlinear stochastic optimal bounded control strategy for random excited hysteretic systems with actuator saturation is proposed. First, a controlled hysteretic system is converted into an equivalent nonlinear nonhysteretic stochastic system. Then, the partially averaged Itoe stochastic differential equation and dynamical programming equation are established, respectively, by using the stochastic averaging method for quasi non-integrable Hamiltonian systems and stochastic dynamical programming principle, from which the optimal control law consisting of optimal unbounded control and bang-bang control is derived. Finally, the response of optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov （FPK） equation associated with the fully averaged Itoe equation. Numerical results show that the proposed control strategy has high control effectiveness and efficiency.     

Stochastic optimal control of first-passage failure for rectangular thin plate vibration model under gaussian white-noise excitations

A rectangular thin plate vibration model subjected to inplane stochastic excitation is simplified to a quasinonintegrable Hamiltonian system with two degrees of freedom. Subsequently a one-dimensional Ito? stochastic differential equation for the system is obtained by applying the stochastic averaging method for quasi-nonintegrable Hamiltonian systems. The conditional reliability function and conditional probability density are both gained by solving the backward Kolmogorov equation numerically. Finally, a stochastic optimal control model is proposed and solved. The numerical results show the effectiveness of this method.     

Markov过程修正的一则注记

随机过程修正广泛应用于研究随机过程，随机流与随机微分系统．在本篇论文中，我们讨论具有Feller半群的Markov过程的修正，并给了Markov过程在状态空间S为非紧时修正定理的证明，并应用此修正定理构造了一个Feller过程的例子．