一、经济:废井田 二、政治和军事:争霸→兼并 三、政治制度:宗法分封→专制官僚 四、社会:世袭→流动 五、学术:贵族→民间 六、结论:

一、FLAC3D软件简介 二、FLAC3D的基本原理 三、FLAC3D的前后处理 四、流-固耦合分析 五、接触单元与应用 六、完全非线性的动力分析 七、自定义本构模型的基本方法 八、结构单元及应用

Lecture D34 Coupled Oscillators Spring-Mass System(Undamped/Unforced)

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

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

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

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

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

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 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