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Topic: Problem with inverse laplace
Replies: 5   Last Post: Mar 19, 2014 11:05 AM

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 Steven Lord Posts: 18,038 Registered: 12/7/04
Re: Problem with inverse laplace
Posted: Dec 7, 2012 9:58 AM

"spv " <krimen_spv@hotmail.com> wrote in message
news:k9qttc\$dki\$1@newscl01ah.mathworks.com...
> 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"

*snip*

> 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.

You may even still remember it, depending on how long it's been since you
learned it in school. The formula is short and easy to read. The cubic
formula? Not so much.

http://en.wikipedia.org/wiki/Cubic_function#Roots_of_a_cubic_function

While Symbolic Math Toolbox _probably_ could expand out the formula using
the formulae on the above Wikipedia page, I highly doubt you'd find it
"usable".

The quartic case is even worse to the point where Wikipedia shows it as an
image rather than text.

http://en.wikipedia.org/wiki/Quartic_equation#Solving_a_quartic_equation

In any case, except for specific equations we'd probably have to use the
above form for quintics and higher.

http://en.wikipedia.org/wiki/Abel%E2%80%93Ruffini_theorem

Finally, just because a PROBLEM is simple to state doesn't mean the ANSWER
is simple to state. Just ask Pierre de Fermat and Andrew Wiles.

http://en.wikipedia.org/wiki/Andrew_Wiles

--
Steve Lord
slord@mathworks.com
http://www.mathworks.com

Date Subject Author
2/13/11 Chaitanya Vichare
2/13/11 Walter Roberson
12/6/12 spv
12/7/12 Steven Lord
3/19/14 vansac
3/19/14 vansac