large Last Multiplier of Generalized Hamilton System

We study an application of the Jacobi last multiplier to a generalized Hamilton system. A partial differential equation on the last multiplier of the system is established. The last multiplier can be found by the equation. If the quantity of integrals of the system is sufficient, the solution of the system can be found by the last multiplier.     

THE MEAN-SQUARE EXPONENTIAL STABILITY AND INSTABILITY OF STOCHASTIC NONHOLONOMIC SYSTEMS

We present a new methodology for studying the mean-square exponential stability and instability of nonlinear nonholonomic systems under disturbance of Gaussian white-noise by the first approximation. Firstly, we give the linearized equations of nonlinear nonholonomic stochastic systems; then we construct a proper stochastic Lyapunov function to investigate the mean-square exponential stability and instability of the linearized systems, and thus determine the stability and instability in probability of corresponding competing systems. An example is given to illustrate the application procedures.     

Birkhoff系统的Poincare—Cartan积分不变量

基于现代微分几何学，分析了作为保守系统和非保守系统的推广－Birkhoff系统的辛结构。构造Birkhoff系统的Poincare-Cartan积分不变量。最后，将一维阻尼振动作为示例，求出其Poincare积分不变量。     

Poisson theory and integration method for a dynamical system of relative motion

This paper focuses on studying the Poisson theory and the integration method of dynamics of relative motion.Equations of a dynamical system of relative motion in phase space are given.Poisson theory of the system is established.The Jacobi last multiplier of the system is defined,and the relation between the Jacobi last multiplier and the first integrals of the system is studied.Our research shows that for a dynamical system of relative motion,whose configuration is determined by n generalized coordinates,the solution of the system can be found by using the Jacobi last multiplier if (2n 1) first integrals of the system are known.At the end of the paper,an example is given to illustrate the application of the results.     

POINCARE-CARTAN INTEGRAL INVARIANTS OF BIRKHOFFIAN SYSTEMS

Based on modern differential geometry, the symplectic structure of a Birkhoffiansystem which is an extension of conservative and nonconservative systems is analyz ed. Anone-dimensional damped vibration is taken as an ilhustrative example and an integralinvariant of Poincaré's type is found.     

Stability with respect to partial variables for Birkhoff systems

In this paper, the stability with respect to partial variables for the Birkhoff system is studied. By transplanting the results of the partial stability for general systems to the Birkhoff system and constructing a suitable Liapunov function, the partial stability of the system can be achieved. Finally, two examples are given to illustrate the application of the results.     

Noether＇s theorem and one-step corrections method for holonomic system

In this paper, a new computational method for improving the accuracy of numerically computed solutions is introduced. The computational method is based on the one-step method and conserved quantities of holonomic systems are considered as kinematical constraints in this method.     

Birkhoff系统的Poincaré-Cartan积分不变量

基于现代微分几何学,分析了作为保守系统和非保守系统的推广--Birkhoff系统的辛结构.构造Birkhoff系统的Poincaré-Cartan积分不变量.最后,将一维阻尼振动作为示例,求出其Poincaré积分不变量.     

Gauss白噪声与非Gauss白噪声

讨论了工程中经常遇到的两种随机过程,即Gauss过程和非Gauss过程,以及与此相关的两类随机积分,Ito积分与Stratonovich积分.对于Gauss过程Ito积分与Stratonovich积分之间存在着Wong-Zakai修正项;而对于非Gauss过程Ito积分与Stratonovich积分之间是否存在修正项,目前尚存争议.     

理论力学可视化教学与Matlab/Simulink

理论力学中的运动学部分有很多机构在教学过程中需要演示给学生观摩,如何用直观而易行的办法来完成该项任务是个值得探讨的问题.而理论力学中的动力学部分,对于系统的建模和分析已有一套解析的办法,但缺乏直观性.本文通过算例演示了Matlab/Simulink中的SimMechanics软件在理论力学教学中的应用.