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

第一节发酵的定义及应用范围 第二节发酵工程组成及硏究内容 第三节发酵工业 第四节发酵方法的类别与流程 第五节我国发酵工业的科技进步

第一节菌种的分离筛选 第二节培养分离 第三节工业微生物育种 第四节菌种的保藏及活化

一、微生物反应过程的主要特征 微生物是该反应过程的主体:是生物催化剂,又是一微小的反应容器。 微生物反应的本质是复杂的酶催化反应体系。酶能够进行再生产

发酵主要设备为发酵罐和种子罐,它们各自都附有原料(培养基)调制、蒸煮、灭菌和冷却设备,通气调节和除菌设备,以及搅拌器等。 种子罐:以确保发酵罐培养所必需的菌体量为目的。 发酵罐:承担产物的生产任务。 它必须能够提供微生物生命活动和代谢所要求 的条件,并便于操作和控制,保证工艺条件的实现,从而获得高产