Ocs package: Difference between revisions

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227 bytes added ,  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}
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>
349

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