Electromechanical Dynamics (Part 1).0051

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Lumped Electromechanical Elements applied voltages, the material properties (polarization), and the geometry. Thus, because (2.1.27) is an integral over space, the charge q is a function of the applied voltages, material properties, and geometry. If we again consider the system in Fig. 2.1.6 and specify that the time variation of the geometry is uniquely specified by a mechanical displacement x with respect to a fixed reference, we can write the charge in the general functional form q = q(v, x). (2.1.29) In writing the charge in this way we have indicated explicit functional dependence on only those variables (v and x) that may be functions of time. We can now use (2.1.29) in (2.1.28) to obtain the terminal current as i q dv + q dx (2.1.30) av dt ax dt The first term exists only when the voltage is changing with time and the second term exists only when there is relative mechanical motion. If we consider a system whose polarization density P is a linear function of field quantities, the system is electrically linear and the
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