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227 bytes added ,  02:00, 22 September 2015
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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 definition of the internal variable in an "implicit form"
+
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}
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</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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