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Electromechanical Dynamics (Part 1).0052

Electromechanical Dynamics (Part 1).0052 - problem to q =...

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__ ___ Circuit Theory We assume that there are M mechanical displacements that uniquely specify the time variation of the geometry X1, X2, •••, XM" Although we write these displacements as if they were translational, they can equally well be rotational (angular). For the integration of (2.1.26) we select a surface S, that encloses the kth equipotential body. Then (2.1.27) is integrated over the enclosed volume V, and the conservation of charge expression (1.1.26) is used to express the current into the terminal connected to the kth equipotential as It = d , (2.1.34) dt where qk = p dV. (2.1.35) Because the system is quasi-static, the fields are functions only of the applied voltages, the material properties, and the displacements. Thus we can generalize the functional form of (2.1.29) for our multivariable
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Unformatted text preview: problem to q = qk(vl, v 2 , • . , VN; xx, x 2 , ... XM), (2.1.36) k= 1,2,. .., N. From (2.1.36) and (2.1.34), the k'th terminal current follows as N aqk dv 1 m aqk dx 1 ik = a + . d , (2.1.37)-1 avj dt j=1 ax dt k=1,2,. .., N. If we specify that our multivariable system is electrically linear (a situation that occurs when polarization P is a linear function of electric field intensity) we can write the function of (2.1.36) in the form N qk CkJx 1 , • 2, ..... XM)Vf, (2.1.38) $=1 k=1, 2,. .. N. Equations 2.1.36 and 2.1.38 can be inverted to express the voltages as functions of the charges and displacements. This process was illustrated for magnetic field systems by (2.1.19) through (2.1.24). 2.1.2 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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