In this lecture, we will revisit the application of Newton's second law to a system of particles and derive some useful relationships expressing the conservation of angular momentum. Center of Mass Consider a system made up of n particles. A typical particle, i, has mass mi, and, at the instant considered, occupies the position Ti relative to a frame xyz. We can then define the center of mass, G, as the point

In this lecture, we will particularize the conservation principles presented in the previous lecture to the case in which the system of particles considered is a 2D rigid body. Mass Moment of Inertia In the previous lecture, we established that the angular momentum of a system of particles relative to the center of mass, G, was

Outline Review of Equations of Motion Rotational Motion Equations of Motion in Rotating coordinates Euler Equations Example: Stability of Torque Free Motion Gyroscopic Motion Euler Angles Steady Precession Steady Precession with M=0 MIT

In this lecture, we will derive expressions for the angular momentum and kinetic energy of a 3D rigid body. We shall see that this introduces the concept of the Inertia Tensor. Angular Momentum We start form the expression of the angular momentum of a system of particles about the center of mass

In this lecture, we will consider how to transfer from one orbit, or trajectory, to another. One of the assumptions that we shall make is that the velocity changes of the spacecraft, due to the propulsive effects, occur instantaneously. Although it obviously takes some time for the spacecraft to accelerate to the velocity of the new orbit, this assumption is reasonable when the burn time of the rocket is much smaller than the period of the orbit. In such cases, the Av required to do the maneuver is simply the difference between the

When the only force acting on a particle is always directed to- wards a fixed point, the motion is called central force motion. This type of motion is particularly relevant when studying the orbital movement of planets and satellites. The laws which gov- ern this motion were first postulated by Kepler and deduced from observation. In this lecture, we will see that these laws are a con- sequence of Newton's second law. An understanding of central

Solution General solution x(t)= A cos wnt +B sin wnt or, x(t)=Csin(wnt+φ) Initial conditions

Lecture D32: Damped Free Vibration Spring-Dashpot-Mass System k Spring Force Fs =-kx, k>0 Dashpot Fd =-cx, c>0 Newton's Second Law (mx =EF) mx +cx+kx (Define)Natural Frequency wn=k/m,and

自动控制广泛地应用于工农业生产,交通运输,国防和航天等各个领域。 随着生产和科学技术的发展,自动控制技术起的作用越来越重要,自动化水平 越来越高,如人造卫星能按预定轨道运行,并能返回地面,导弹能正确的命中 目标,宇宙飞船能准确在目标上着陆,并能返回地球。这都是由于自动控制技 术高速发展的结果

一、国际贸易理论部分的主要内容 二、资本主义发展阶段国际商品运动的一般规律。资本主义的发展推动了国际贸易的发展。 三、国际贸易理论和学说研究商品和劳务在国际间流动的原因、动向及流动结果,从而揭示国际贸易产生、发展和贸易利益分配过程中的特点和运动规律的学科