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Electromechanical Dynamics (Part 1).0095

Electromechanical Dynamics (Part 1).0095 - of charge leads...

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Lumped-Parameter Electromechanics to replace the first term on the right-hand side of (3.1.38). Rearranging terms, we obtain N M dW~ = A s di, + If," dx,, (3.1.40) 1=1 $=1 where N W,' = ji - W• (3.1.41) j=1 and W,' is the coenergy. The independent variables are (iQ, i, . . . N; x,, x,, .. . ,~Ux). We assume that the A's and W, in (3.1.41) are written in terms of these variables, hence that W' is a function of these variables. Then N aw' M aw' dW. = - di, + dx,, (3.1.42) J=1 ai, -=1 ax, and when we subtract (3.1.42) from (3.1.40) and require that the coefficient of each di, and each dxj be zero aw' A i = ; j = 1, 2,. N, (3.1.43) ai 1 f" = - ' ; j = 1, 2, . .. , M. (3.1.44) axj This same process of generalization can be carried out for an electric field system (see Table 3.1); for instance, for the system of N electrical terminal pairs and M rotational mechanical terminal pairs for which the torque was found in (3.1.27) the use of the voltage as the independent variable instead
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Unformatted text preview: of charge leads to the result Te = awe'(V', V 2 , .... VN; 01, 02. .... ) M) aoi , (3.1.45) a0, where N We' = ,v 1 q -We. (3.1.46) 1=1 This expression is obtained by a straightforward process of exactly the same form as that used for the general magnetic field system (3.1.38) to (3.1.44). It is not necessary to find the coenergy by first determining the energy; for example, we can integrate (3.1.32) to find W' just as we integrated (3.1.9) to find W,. In general, we evaluate W, by selecting a path of integra-tion through variable space for (3.1.40) that changes the xz's with all electrical excitations zero and then changes electrical excitations with mechanical displacements held fixed. For a better understanding of the meaning of coenergy consider the A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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