The mathematical model is
$$V'=\frac{I}{C}, V(0)=0$$ and $$I'=\frac{-V}{L}-\frac{RI}{L}+\frac{V_β}{L}, I(0)=0$$ With I.C $V_β=5 V, R=0.1Ω, L=4*10^{-9}H and C=0.5*10^{-9}F $
I have calculated and I have found that the differential has one equilibrium point $(V_eq,I_eq)=(5,0)$.
Now I want to find The characteristic equation for the eigenvalues of the Jacobian matrix.
I use the following code but no result! Where have i done the mistake?
vb = 5; r = 0.1; l = 4*Power[10, -9]; c = 0.5*Power[10, -9];
f = i/c;
g = (-v/l) - (r*i/l) + vb/l;
deq1 = v'[t] == f
deq2 = i'[t] == g
equilibrio = Solve[{f == 0, g == 0}, {v[t], i[t]}]
MatrixForm[jacobian = D[{f, g}, {{v[t], t[t]}}] // Simplify]
Simplify[MatrixForm[jacobian] /. equilibrio]
v
andi
, notv[t]
andi[t]
. You should change that inSolve
. $\endgroup$