In this lecture, we will revisit the principle of work and energy introduced in lecture D7 for particle dynamics, and extend it to 2D rigid body dynamics. Kinetic Energy for a 2D Rigid Body We start by recalling the kinetic energy expression for a system of particles derived in lecture D17

In lecture D9, we saw the principle of impulse and momentum applied to particle motion. This principle was of particular importance when the applied forces were functions of time and when interactions between particles occurred over very short times, such as with impact forces. In this lecture, we extend these principles to two dimensional rigid body dynamics. Impulse and Momentum Equations Linear Momentum In lecture D18, we introduced the equations of motion for a two dimensional rigid body. The linear momen- tum for a system of particles is defined

In this lecture, we consider the motion of a 3D rigid body. We shall see that in the general three dimensional case, the angular velocity of the body can change in magnitude as well as in direction, and, as a consequence, the motion is considerably more complicated than that in two dimensions. Rotation About a Fixed Point We consider first the simplified situation in which the 3D body moves in such a way that there is always a point, O, which is fixed. It is clear that, in this case, the path of any point in the rigid body which is at a

A pendulum is a rigid body suspended from a fixed point (hinge) which is offset with respect to the body's center of mass. If all the mass is assumed to be concentrated at a point, we obtain the idealized simple pendulum. Pendulums have played an important role in the history of dynamics. Galileo identified the pendulum as the first example of synchronous motion, which led to the first successful clock developed

D244BD RIGID BODY DYNAMICS KINETIC EWEGY In echure we derwed am kinenc a susem u dm T= Fere ts the velouty relanve to G. for a nald body we ca wate Uing the vechor nidontklyAxB=Ax

In this lecture, we consider the problem of a body in which the mass of the body changes during the motion, that is, m is a function of t, i.e. m(t). Although there are many cases for which this particular model is applicable, one of obvious importance to us are rockets. We shall see that a significant fraction of the mass of a rocket is the fuel, which is expelled during flight at a high velocity and thus, provides the propulsive force for the rocket

MATLAB语言是一种广泛应用于工程计 算及数值分析领域的新型高级语言,自1984 年由美国 Math Works公司推向市场以来, 历经十多年的发展与竞争,现已成为国际公 认的最优秀的工程应用开发环境。 MATLAB功能强大、简单易学、编程效率 高,深受广大科技工作者的欢迎

1920年,美国物理学家康普顿在观察X射线被物质 散射时,发现散射线中含有波长发生变化了的成分

一、西方美学史的研究对象和范围 严格说,美学史应当是世界美学史,它应当既包括西方美学史,又包括东方美学史。但 时至今日,还没有出现一部世界美学史我们讲的西方美学史,只是世界美学史的一部分。 “西方”两字主要指欧洲各国,还有美国和俄国;它只是一个地域性的概念,不是政治概念。 西方古典美学史主要是欧洲美学史

教学是在教育目的的规范下,由教师的 教”与学生的“学”共同组成的教育活动, 通过教学,学生在教师有目的、有计划的指 导下,积极、主动地掌握系统文化科学知识 和技能,发展能力、增强体质,陶冶美感, 形成一定的思想品德和个性。 教学的实质是以知识的传授为基础,促 进学生身心的健康发展