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Line 534: | Line 534: | ||
The first thing to do is to change the model from impedance to admittance form | The first thing to do is to change the model from impedance to admittance form | ||
and write the | and write the constitutive relation for the internal variable in an "implicit form" | ||
<math> | <math> | ||
\left\{ | \left\{ | ||
\begin{array}{l} | \begin{array}{l} | ||
Q(V(t), x(t)) = \dfrac{1}{\mu} \dot{x} - I(t) = 0\\ | \dfrac{1}{\mu} \dot{x} + Q(V(t), x(t)) = \dfrac{1}{\mu} \dot{x} - I(t) = 0\\ | ||
H(x) = \left\{ | H(x) = \left\{ | ||
\begin{array}{l} | \begin{array}{l} | ||
Line 552: | Line 552: | ||
</math> | </math> | ||
It is then useful to compute the derivatives | It is then useful to compute the derivatives for the current and for the constitutive relation | ||
<math> | |||
\dfrac{\partial I}{\partial x} = -\dfrac{H'(x)}{H(x)^2} | |||
</math> | |||
<math> | |||
\dfrac{\partial I}{\partial V} = \dfrac{1}{H} | |||
</math> |
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