一、模拟的应用 1、工程设计 2、虚拟环境 3、模型验证 二、课程原理 三、问题实例 1、集成电路的功率分配 2、空间结构的受力关系 3、插件的温度分布

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

Lecture D33: Forced Vibration Fosinwt m Spring Force Fs =-kx, k>0 Dashpot Fd =-ci, c>0 Forcing Fext Fo sin wt Newton's Second Law (mix =CF) mx+cx+kx= Fo sin wt =k/m,=c/(2mwn)

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

In lecture D28, we derived three basic relationships embodying Kepler's laws: Equation for the orbit trajectory

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 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

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

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