Hi again,
That linked site looks very interesting, i'll have to spend a bit more time reading there i think.
I havent used that particular kind of analysis, but generally defining the capacitor a bit different than usual sometimes leads to an immediate simplification in the equations, so for that method they may want to base that part of the analysis on charge rather than current or voltage directly. This is usually achieved by using:
i=dq/dt
What this does is an expression defined in terms of current of the form:
v=i*R
turns into;
v=R*dq/dt
and for an inductor instead of:
v=L*di/dt
we have:
v=L*d^2q/dt^2 (now a second derivative)
so an integrodifferential equation like this:
V=R*i+L*di/dt+(1/C)*Integral(i) dt
turns into:
V=R*dq/dt+L*d^2q/dt^2+q/C
So we got to a pure differential equation simply by swapping out all i=dq/dt, and the capacitance now enters as a constant.
Also, starting with:
dv/dt=i/C
we get:
dv/dt=(dq/dt)/C
or:
dv/dt=dq/(C*dt)
or:
dv=dq/C
or:
dv/dq=1/C
so we end up with the capacitance defined in terms of charge and voltage.
This i believe would help with a general non linearity of the capacitor, but to get the full explanation i think maybe you should contact:
jens.flucke@gmail.com
If you can get one complete full analysis example from him (or someone else at that site) we could follow it through from start to finish and see how it goes.