Analytical dynamics : theory and applications by Mark D Ardema

By Mark D Ardema

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The second way is to determine the motion when the forces are given (problem of the first kind). This situation typically arises in the performance estimation of an existing system. For example, it may be of interest to determine the range of orbits accessible by an existing launch vehicle. In this book we approach dynamics as a problem of the first kind, although all the results obtained apply equally to either type of problem. Thus it is characteristic that the equations of motion of a particle system give the accelerations of the particles in terms of their positions, velocities, and time.

Now introduce linearly independent unit vectors {ei, 62,63}. Then, if {ei, 62, 63} are fixed in the inertial frame. 6) Note the interpretations of rrig and Fg] for example, m i , m2, and ma are all the mass of the first particle and Fi, F2, and F3 are the three components of the resultant force acting on the first particle. 2 Motion Representation C o n f i g u r a t i o n S p a c e . 7) \ UN J We call C the configuration space. As the motion of the system proceeds, a p a t h is generated in this space called a C trajectory.

Point A is either G, the center of mass, or moves with constant velocity in the inertial frame; and 2. Axis k is an axis of rotational mass symmetry or the body is "thin". Concepts of 3-D kinetics will be introduced as needed in future Chapters. Work and Energy for Rigid Body. As before, Eqn. 44) applies, repeated here: Aro,i + AFo,i = t/o"? 54) For most of the approaches to dynamics developed later in this book, an essential step in deriving the equations of motion of a dynamic system is the determination of the system's kinetic energy.

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