Can anbody solve this simple equation?
1 vue (au cours des 30 derniers jours)
Afficher commentaires plus anciens
Hello everybody.I have attached the equation 1 and equation 2 in picture,How the values on right hand side are obtained, can anybody write it step by step.I will be very thankful.Please ignore the the X and 0 in Rg(0) anf Rg(X)
1 commentaire
Réponse acceptée
Stephan
le 10 Sep 2018
Modifié(e) : Stephan
le 13 Sep 2018
Hi,
to obtain values from your function use this:
fun_rg = @(R_g0,sigma_1,sigma_2,x)exp((x.^2.*(R_g0.^2-1.0).^2.*(1.0./2.0))./(R_g0.^2.*sigma_1.^2-R_g0.^2.*sigma_2.^2)).*sqrt(R_g0.^2)
This function handle takes values for: Rg(0), σ1, σ2 and x and gives back the value for Rg(x). For example with:
Rg(0) = 1.25
σ1 = 10
σ2 = 25
x = 3
>> fun_rg(1.25,10,25,3)
ans =
1.2478
The code to get this function is:
syms sigma_b sigma_1 sigma_2 R_g(x) R_g0
a = sqrt((sigma_b^2 + sigma_2^2) / (sigma_b^2 + sigma_1^2))
b = (sigma_2^2 - sigma_1^2) * x^2
c = 2 * (sigma_b^2 + sigma_2^2) * (sigma_b^2 + sigma_1^2)
fun_sigma_b = sqrt((sigma_2^2 - R_g0^2 * sigma_1^2) / (R_g0^2 -1))
fun_Rg_x = R_g(x) == a * exp(-b/c)
fun_Rg_x = simplifyFraction(subs(fun_Rg_x,sigma_b, fun_sigma_b))
fun_rg = matlabFunction(rhs(fun_Rg_x))
where a,b,c are stepwise written parts of the equation for Rg(x), so that Rg(x) can be written in the form:
R_g(x) = a * exp(-b/c)
This step is not neede but helps seeing what happens. To see the results in a more mathematical notation have a look at the file attached.
EDIT :
To get the result from equation 2 starting from equation 1 use:
syms sigma_b sigma_1 sigma_2 R_g(x) R_g0
a = sqrt((sigma_b^2 + sigma_2^2) / (sigma_b^2 + sigma_1^2))
b = (sigma_2^2 - sigma_1^2) * x^2
c = 2 * (sigma_b^2 + sigma_2^2) * (sigma_b^2 + sigma_1^2)
fun_Rg_x = R_g(x) == a * exp(-b/c)
fun_Rg_x = subs(fun_Rg_x,x,0)
fun_Rg_x = simplify(expand(isolate(fun_Rg_x,sigma_b)))
This will give the equation as you wanted. The mathematical notation is attached as a .pdf-file.
Best regards
Stephan
3 commentaires
Plus de réponses (0)
Voir également
Catégories
En savoir plus sur Equation Solving dans Help Center et File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!