mu Xuu+ Xww-mg cos 000+ m(wi-qUo) Zuu+ Zww Ziw+ Zgq-mg sin+ Iyyq Muu+ Mww+ Mww+ Mq+ There is no roll/yaw motion, so=0. Control commands△x,△z,and△ MC have not yet been specified

Static stability is all about the initial tendency of a body to return to its equilibrium state after being disturbed To have a statically stable equilibrium point, the vehicle must develop a restoring force/ moment to bring it back to the eq. condition Later on we will also deal with dynamic stability, which is concerned with the time history of the motion after the disturbance

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

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

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

Longitudinal equations (1-15) can be rewritten as: mu Xuu+ Xww-mg cos 0+ m(w-qUo) =Zuu+ Zww+ Zq-mg sin 000+Z Iyyg =Muu+ Mww+ Mw++ There is no roll/yaw motion, so q 0

Inertial reference frames In the previous lecture, we derived an expression that related the accelerations observed using two reference frames, A and B, which are in relative motion with respect to each other. aA =aB+(aA/ B)'y'' 22 x (DA/ B) 'y'2'+ TA/B+ X TA/B). (1) Here, aA is the acceleration of particle A observed by one observer, and

In this lecture we will consider the equations that result from integrating Newtons second law, F=ma, in time. This will lead to the principle of linear impulse and momentum. This principle is very useful when solving problems in which we are interested in determining the global effect of a force acting on a particle over a time interval Linear momentum We consider the curvilinear motion of a particle of mass, m, under the influence of a force F. Assuming that

Chapter 5 Uniform Circular Motion Macintosh PICT image format is not supported What does it mean? How do we describe it? What can we learn about it

§2.1 牛顿运动三定律 §2.2 力学中常见的几种力 §2.3* 基本的自然力 §2.4 牛顿运动定律应用举例 §2.5 非惯性系与惯性力