理论力学刚体的基本运动7.ppt

1 〔Example 5〕Draw the velocity and acceleration vectors of the pointsＭ and Ｎ on the rigid bodies shown in the following figures. 〔例5〕试画出图中刚体上Ｍ?Ｎ两点在图示位置时的速度和 加速度。 O 〔Example6〕Referring to the figure, a projectile is fired from the point O with an angle of elevation . Show that the angle under which the projectile reaches the line L in the shortest time is . 〔例6〕已知如图，从O点以 任一角度抛出一质点，试证明 质点最早到达直线Ｌ的抛角为　 。 ? O ? 到达高度为 h 时，t 与　的 关系有下式确定 For y = h, the relation between t and is 解：选　　坐标系，则 Proof：choosing the coordinate system , we get To minimize the time you have to solve ? 欲使最早到达，必须满足 ? which gives the angle for the shortest time which the projectile takes from O to the line L. 表示出在某一角度下时间会最短。（极值） 又 证毕。 将?对　求导数 The derivative of ? with respect to gives 将　　　（最早到达的条件）代入?，得　　　　 Inserting 　　　 into ? yields　　　　 三.链轮系: 设有： A,B,C,D,E,F,G,H 轮系,则总传动比： Pulley system: For a system consisting of pulleys A,B,C,D,E,F,G,H , the transmission ration of the pulleys A to H is given by： 其中m代表外啮合的个数；负号表示最后一个轮转向与第一个轮转向相反。 where m represents the number of the pulleys, and the negative sign indicates that the rotation direction of the last pulley is opposite to that of the first one. §7–5 Vector representation of angular velocity and angular acceleration §7-5 角速度和角加速度的矢量表示 点的速度和加速度的矢量表示 1. Vector representation of angular velocity and angular acceleration: 一. 角速度和角加速度的矢量表示 The directions of and are determined according to the right-hand rule. 按右手定则规定 ， 的方向。 Magnitude: 2. Vectorial representation of the linear velocity and acceleration of any point in a rigid body 二 刚体内任一点的线速度和线加速度的矢积表示 Basic concepts, features of motions and equations 一.基本概念和基本运动规律及基本公式 Chapter 6: Kinematics of a particle Chapter 7: Basic motions of a rigid body Lesson for problem solving 第六章 点的运动学, 第七章 刚体的基本运动 习题课 2) Basic features of motions and basic equations: 2. 基本运动规律与公式: 1) Basic concepts：rectilinear motion, curvilinear motion (of