"spv " <email@example.com> wrote in message news:firstname.lastname@example.org... > that the roots of the polynomial are complex is quite obvious because this > kind of equation represent the transient of an electric system (active and > reactive parts), the problem is that matlab is perfectly able to compute > ilaplace over a (polynomial of degree <=2) divided by a (polynomial of > degree <=2) but when the function on the denominator grows one degree it > return this kind "result"
> inc_w2_i = ilaplace(inc_w2); > > the result of this is: > > -(25132*sum(exp(r4*t)/(11000*r4 - 168000*r4^2 + 15566), r4 in > RootOf(s4^3 - (11*s4^2)/112 - (7783*s4)/28000 - 6283/8000, s4)))/5 > > Completely unusable, if I apply vpa() to this result I get a sum of > exponentials, it might be ok but it is not, for this result to be usable, > we have to apply euler's equation: exp(x+iy)=exp(x)*(cos(y) + i*sin(y)) > which is not possible because the result is a symbolic type. (at least I > couldn't) > > but if we downgrade the equation: > > inc_w2= inc_P_L1*((-T)/((M1*s+D1)*((M2*s+D2)+T)+(M2*s+D2)*T)); > inc_w2_i = ilaplace(inc_w2) > > the result is now something quite usable : > > (25132*2712531089^(1/2)*sinh((2712531089^(1/2)*t)/56000)*exp((9033*t)/56000))/13562655445 > > a function that effectively represents the transient of a sinusoidal wave. > > So after googling a lot I have not seen a proper answer to this issue.
I think most people are familiar with the quadratic formula that is taught in schools.