THE EQUATIONS OF MOTION OF A SYSTEM UNDER THE ACTION OF THE IMPULSIVE CONSTRAINTS

In order to solve the problem of motion for the system withn degrees offreedom under the action of p impulsive constraints, we must solve the simultaneous equations consisting of n+p equations. In this paper, it has been shown that the undetermined multipliers in the equations of impact can be cancelled for the cases of both the generalized coordinates and the quasi-coordinates. Thus there are only n-p equations of impact. Combining these equations with p impulsive constraint equations, we have simultaneous equations consisting of n equations. Therefore, only n equations are necessary to solve the problem of impact for the system subjected to impulsive constraints. The method proposed in this paper is simpler than ordinary methods.     

标准化的磁撞方程

标准化的磁撞方程孙右烈（上海大学力学教研组，上海２０００２７）１引言考虑具有ｎ个广义坐标ｐ＿ｉ，ｉ＝１，２，…，ｎ，加有ｓ个非线性非完整约束（也可以是非线性非完整冲击性约束）的系统，其上作用有广义冲力根据非线性非完整系统的Ｒｏｕｔｈ方程￣［１］可知由...     

THE EQUATIONS OF MOTION FOR A NONHOLONOMIC SYSTEM UNDER THE ACTION OF IMPULSIVE FORCES

The equations of impact for a nonholonomic system described with generalizedcoordinated have been discussed in detail in the general references of classical dynamics.But these equations contain undetermined multipliers which made the problem complicatedThrough the appropiate treatment of mathematics,using the δ-function andexpression of matrix in this paper,the author derived equations of impact for anonholonomic system without undetermined multipliers.Therefore.the problem can besolved more simply.     

碰撞问题中恢复系数k的三个等价表达式

在求解刚体的碰撞问题时,需要引入恢复系数k。本文提出以碰撞二个阶段中的碰撞冲量之比作为恢复系数的基本定义,据此导出k=(-((E_2)/(E_1))~(1/2)和一般理论力学中所采用的恢复系数公式;并说明这三种表达式是等价的。从而使恢复系数的物理意义更加清晰。     

非完整系统的马基方程中转换矩阵C的一般形式

在受冲力作用的非完整系统的运动方程和受冲击性约束作用的系统的运动方程中,非完整约束对系统的作用取决于一个特殊形式的矩阵C,这在有关的文献[1][2]里巳涉及到了。本文进一步阐明矩阵C的存在性及其一般形式。     

运动状态空间中的变分原理

本文考虑有热交换现象存在时的连续介质的运动问题,提出用广义速度v_i,(i=1,2,3)以及绝对温度T 来描写其运动状态,简称运动状态空间;并根据能量守恒定律,将分析力学中的速变空间中的变分原理,推广至运动状态空间中,建立了运动状态空间中的变分原理,从而可以推出运动状态空间中的四个动力学方程. ...     

非线性非完整系统的运动方程及其广义能量积分

本文研究了一阶非线性非完整系统的运动规律,由 Routh 方程出发,用了矩阵的右乘零因子的有关理论,给出了该系统的不含待定乘子的一般方程,本文还讨论了一阶非线性非完整系统的运动方程存在广义能量积分的条件,并给出了相应的广义能量积分.     

由哈密顿原理导出Navier-Stokes方程

本文用分析力学中的哈密顿原理导出了Nav-ierStokes 方程,并给出了连续介质的拉格朗日方程.     

The equations of motion for a nonholonomic system under the action of impulsive forces

The equations of impact for a nonholonomic system described with generalized coordinated have been discussed in detail in the general references of classical dynamics. But these equations contain undetermined multipliers which made the problem complicated. Through the appropriate treatment of mathematics, using the -function and expression of matrix in this paper, the author derived equations of impact for a nonholonomic system without undetermined multipliers. Therefore, the problem can be solved more simply.