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Advance Dynamics: Modeling and Analysis by A. Frank D'Souza

By A. Frank D'Souza

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W .. "<:: = * r ........ \ 1¥\,_ Since ; x m~ = constant, the motion takes place in a plane defined by some initial position vector; and initial velocity vector~. The constant vector It is of course perpendicular to this plane. Employing polar coordinates to represent this plane motion, we have ; ri r and ~ = ; 1r + rfii e. as shown in Chapter 2. 58) it is seen that A constant. This is the statement of Kepler's second law for planetary motion, which is stated later in this chapter.

We consider a rigid body which has angular velocity vector with respect to an inertial frame XYZ (Fig. 1). The coordinate system, Oxyz, has its origin ~t a reference point, 0, of the body and it rotates at ~e same angular velocity w as the body. Such a coordinate system, Oxyz, is called a body coordinate system. 1) The position vector R of the point P with respect to the inertial coordinate system X YZ is the vector sum of R. 1 INTRODUCTION R = R. +; This chapter is devoted to the study of dynamics of rigid bodies by the direct application of Newton's second law.

Show that the velocities of the vehicle just before and after firing of retro rockets are given by 3GM)I/2 ( -rA- VA and Vc GM)t;z ( - rA where M is the mass of Saturn. 9. A satellite in circular orbit around the earth at an altitude of 1130 km is to be given a new orbit (Fig. 9). The engines are aligned radially, imparting an additional velocity of 4 km/s to the satellite outward. Determine the eccentricity e of the orbit. Is the orbit open or closed? ~ Sec. 2 4 principal axes and principal moments of inertia are discussed.

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