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These equations may be combined at nodes 2 and 3 according to (2.2.33) to eliminate the forces at those nodes (which are not of interest). (dX 2
K2(xl x2) = B dt dx 3 dt ) + K(x 2 - x3) + M
M 2 dx 2 2 dt2 (d) ( Bdt - d) + K 1 (x 2 - x 3 ) = d X (e) With the specified position source x1 = x(t), (f) (d) and (e) can be solved for x 2 and x3 . Then the forcef, applied to the tires by the road can be found from (a) as f. =f, = K 2(x - 2 )(g) Note that the forces acting on the reference in the network diagram do not balance but equal f,. It is presumed that the force transmitted to the earth by the automobile tires will not move the earth. 2.3 DISCUSSION In this chapter we have laid the foundation for studying lumped-parameter electromechanics by reviewing the derivations of lumped electric circuit elements, by generalizing the derivations to include the effects of mechanical motion, and by reviewing the basic definitions and techniques of rigidbody mechanics. The stage is now set to include the electromechanical coupling network of Fig. 2.0.1 and to study some general properties of electromechanical systems, including the techniques for obtaining complete equations of motion.
2.1. A piece of infinitely permeable magnetic material completes the magnetic circuit in Fig. 2P.1 in such a way that it is free to move in the x- or y-direction. Under the assumption that the air gaps are short compared with their cross-sectional dimensions (i.e., that the fields are as shown), find I(x, y, i). For what range of x and y is this expression valid? 0 -0 + x
Depth D into paper Fig. 2P.1 ...
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- Fall '11