integral solver give a function as result

Hi everybody, I am trying to solve my code by using the integral solver of Matlab, since I need to guarantee an energetic equivalence between two graphs. But the result isn't satisfying. The thing is that I cannot understand what's going wrong.

this is the code:

Sig_Height=0.0213*(vel_wind_R^2);

T_zc=0.519*vel_wind_R;

AA=4*pi^3*(Sig_Height/(T_zc^2))^2;

BB=16*pi^3*(1/(T_zc)^4);

syms freq_wave;

Spectre=AA/(freq_wave^5)*exp(-BB/(freq_wave^4)); %Bretschneider's spectre

integral=int(Spectre/(1-2*freq_wave*cos(teta_1rad)/g),0,inf);

Spectre_e=double(integral);

integral_2=int(freq_wave-(freq_wave^2*vel_nave/g)*cos(teta_1rad),0,Inf);

freq_e=double(integral_2);

I specify that:

vel_wind_R= 6.7; teta_1rad= 1.04; g=9.81.

Thanks in advance to whoever will give me support.

Answer 1

[Ishu]

Hi Gianluca Angelini,

I understand that you are trying to solve the equations using "integral" but in the provided code you have not used the "intergral" of MATLAB anywhere.

I tried to reproduce the error at my end and I found that "double()" is not used properly. The functionality of "double()" is to convert symbolic values into doubles but as in the equations there is no value provided for "freq_wave" symbolic varible so it gives error. Therefore, before using "double()" you should use "subs()" to assign a symbolic value to "freq_wave" and then use "double()".

    vel_wind_R= 6.7;
    teta_1rad= 1.04;
    g=9.81;
    Sig_Height=0.0213*(vel_wind_R^2);
    T_zc=0.519*vel_wind_R;
    AA=4*pi^3*(Sig_Height/(T_zc^2))^2;
    BB=16*pi^3*(1/(T_zc)^4);
    
    syms freq_wave
    Spectre=AA/(freq_wave^5)*exp(-BB/(freq_wave^4));        %Bretschneider's spectre
    integral=Spectre/(1-2*freq_wave*cos(teta_1rad)/g);
    Spectre_e=subs(integral, freq_wave, pi);  % replace freq_wave with pi
    Spectre_e2 = double(Spectre_e)

Spectre_e2 = 0.0036

You can refer below documentations for more information:

subs: https://www.mathworks.com/help/symbolic/subs.html?searchHighlight=subs&s_tid=srchtitle_support_results_1_subs

integral: https://www.mathworks.com/help/matlab/ref/integral.html?searchHighlight=integral&s_tid=srchtitle_support_results_1_integral

double: https://www.mathworks.com/help/symbolic/sym.double.html?searchHighlight=double&s_tid=srchtitle_support_results_2_double

Hope it helps.