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Electromechanical Dynamics (Part 1).0040

Electromechanical Dynamics (Part 1).0040 - geometry We are...

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2.1.1 Circuit Theory 19 (2.1.8) and rewrite (2.1. 7) as contour and will not be defined unambiguously. For convenience we define the flux linkage A of the circuit as A = LB.nda (2.1.9) dJ. v=-. dt In a quasi-static magnetic-field system the magnetic flux density is deter- mined by (1.1.20) to (1.1.22) of Table 1.2 and a constitutive law, fc dl = f/f· n da, (1.1.20) fsB. n da = 0, (1.1.21) f/f. n da = 0, (1.1.22) B = ,uo(H + M). (1.1.4) (The differential forms of these equations can also be employed.) In the solution of any problem the usual procedure is to use (1.1.22) first to relate the terminal current to current density in the system and then (1.1.20), (1.1.21), and (1.1.4) to solve for the flux density B. The resulting flux density is a function of terminal current, material properties (1.1.4), and system geometry. The use of this result in (2.1.8) shows that the flux linkage A is also a function only of terminal current, material properties, and system geometry. We are interested in evaluating terminal voltage
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Unformatted text preview: geometry. We are interested in evaluating terminal voltage by using (2.1.9); thus we are interested in time variations of flux linkage A. If we assume that the system geometry is fixed, except for one movable part whose position can be described instantaneously by a displacement x with respect to a fixed refer-ence, and we further assume that M is a function of field quantities alone (and therefore a function of current), we can write A = AU, x). (2.1.10) (2.1.11) In this expression we have indicated explicit functional dependence only on those variables (i and x) that may be functions of time. We can now use (2.1.10) in (2.1.9) and expand the time derivative to obtain v = dJ, = 0), di + OA dx . dt oi dt ox dt This expression illustrates some general terminal properties of magnetic A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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