By G. Franklin, J. Powell, M. Workman

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**Extra info for Digital Control of Dyanmic Systems**

**Sample text**

Many authors follow the original terminology of Maxwell, with some slight modiﬁcations. For instance, Stratton [187] calls E the electric ﬁeld intensity, H the magnetic ﬁeld intensity, D the electric displacement, and B the magnetic induction. Jackson [91] calls E the electric ﬁeld, H the magnetic ﬁeld, D the displacement, and B the magnetic induction. Other authors choose freely among combinations of these terms. For instance, Kong [101] calls E the electric ﬁeld strength, H the magnetic ﬁeld strength, B the magnetic ﬂux density, and D the electric displacement.

Materials that are good dielectrics over broad ranges of frequency include various glasses and plastics such as fused quartz, polyethylene, and teﬂon. Materials that are good conductors over broad ranges of frequency include common metals such as gold, silver, and copper. For dispersive linear isotropic materials, the constitutive parameters become nonstationary (time dependent), and the constitutive relations involve time operators. 28) retain their product form in the frequency domain, then by the convolution theorem we have in the time domain the constitutive relations D(r, t) = E(r, t) + 0 B(r, t) = µ0 H(r, t) + J(r, t) = t −∞ t −∞ t χe (r, t − t )E(r, t ) dt −∞ χm (r, t − t )H(r, t ) dt σ (r, t − t )E(r, t ) dt .

For dispersive linear isotropic materials, the constitutive parameters become nonstationary (time dependent), and the constitutive relations involve time operators. 28) retain their product form in the frequency domain, then by the convolution theorem we have in the time domain the constitutive relations D(r, t) = E(r, t) + 0 B(r, t) = µ0 H(r, t) + J(r, t) = t −∞ t −∞ t χe (r, t − t )E(r, t ) dt −∞ χm (r, t − t )H(r, t ) dt σ (r, t − t )E(r, t ) dt . 31) These expressions were ﬁrst introduced by Volterra in 1912 [199].