广义Birkhoff方程的积分方法

场方法和最终乘子法是求解运动微分方程的基本方法.本文将这两种方法应用于广义Birkhoff系统,求出了场方法的基本偏微分方程和该方程的完全积分;根据Jacobi最终乘子定理求出了广义Birkhoff方程的解.并举例说明结果的应用.     

一阶Lagrange系统的梯度表示

研究一阶Lagrange系统的梯度表示. 给出一阶Lagrange系统可成为梯度系统的条件. 利用梯度系统的性质研究系统的稳定性. 给出例子说明结果的应用. 关键词： 一阶Lagrange系统 梯度系统 稳定性     

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.     

Lagrange系统Lie点变换下的共形不变性与守恒量

研究Lagrange系统Lie点变换下的共形不变性与守恒量,给出Lagrange系统的共形不变性定义和确定方程,讨论系统共形不变性与Lie对称性的关系,得到在无限小单参数点变换群作用下系统共形不变性同时是Lie对称性的充要条件,导出系统相应的守恒量,并给出应用算例. 关键词： Lagrange系统 Lie点变换 共形不变性 守恒量     

PERTURBATION TO THE SYMMETRIES AND ADIABATIC INVARIANTS OF HOLONOMIC VARIABLE MASS SYSTEMS

The perturbation problem of symmetries for the holonomic variable mass systems under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then the corresponding inverse problem is studied. Finally an example is presented to illustrate these results.     

EFFECTS OF NONHOLONOMIC CONSTRAINT ON LIE SYMMETRIES AND CONSERVED QUANTITIES OF LAGRANGIAN SYSTEMS

After a Lagrangian system is constrained by nonholonomic constraints, the determining equations, the structure equation and the form of conserved quantities corresponding to the Lie symmetries will change. Some symmetries vanish and under certain conditions some Lie symmetries still remain.     

A field method for integrating the equations of motion of nonholonomic controllable systems

This paper presents a field method for integrating the equations of motion of nonholonomic controllable systems. An example is given to illustrate the application of the method.     

高阶非完整系统运动方程的一类积分

本文给出高阶非完整系统运动方程的一类积分及其存在条件,包括1阶积分(广义能量积分),2阶积分和p(p>2)阶积分,所有这些积分都可按系统的Lagrange函数来构造.举例说明本文方法的应用.     

Mac-Millan方程对非线性非完整力学系统的推广

本文首先将Mac-Millan方程推广到最一般的非完整力学系统,得到非线性非完整系统的广义Mac-Millan方程.其次,证明广义Mac-Millan方程与广义Чаплыгин方程的等价性,最后给出一个例子.     

变质量完整力学系统的Lie对称与守恒量

研究变质量完整系统的Lie对称和守恒量。利用常微分方程在无限小变换下的不变性建立系统Lie对称的确定方程。给出结构方程和守恒量。举例说明结果的应用。