Find real positive roots of 9th order polynomial
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Hi,
I am trying to find the real positive roots of a 9th order polynomial equation using roots . My program is given below
clear all
close all
clc
%%%% Parameters %%%%
gamma=0.0783;
zai=0.025;
fo=0.25;
f1=0.01;
om_data=.01:.001:0.9;
n=length(om_data);
cnt=1;
cnt1=1;
for ii=1:1:n
A=[];
sol=[];
om=om_data(ii);
P=[25*gamma^3 0 -20*gamma^2*om^2 -15*gamma^2*fo +4*gamma*om^2*(om^2+4*zai^2) ...
16*gamma*fo*om^2 3*gamma*(2*f1^2-3*fo^2) -4*fo^2*om^2*(om^2+4*zai^2) ...
4*fo^2*om^2 -fo^3]; % Polynomial Coefficients
sol=roots(P); % Roots of polynomial
A=sol(imag(sol)==0 & sol>=0); % Select real and positive roots
no_A=length(A);
if no_A==1
plot(om,A,'.');
hold on
elseif no_A==3
om_same = om*ones(1,3);
plot(om_same,A,'.')
hold on
elseif no_A==5
om_same2 = om*ones(1,5);
plot(om_same2,A,'.')
hold on
end
end
The plot which I obtained is different from the actual answer. The correct plot is (I. Kovacicetal et. al. Int. J. Non-linear Mech. 43, 2008)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/460820/image.jpeg)
Q.1 Is there any limitation with the roots command or is there any problem with my code.
Q.2 For fo=0.2 and f1=0.1 the plot should look like this
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/460825/image.jpeg)
That is, there are some parametric region where we obtain multiple roots. But my program is giving a differen plot.
Any help please
Thank You.
6 个评论
Mathieu NOE
2020-12-15
hi
I suppose both options work as soon as this publication is not covered by any NDA or other restrictions
if you prefer , you can send it to : mathieu.noe@hutchinson.com
回答(1 个)
Matt J
2020-12-15
编辑:Matt J
2020-12-15
The roots of a polynomial become increasingly sensitive to small variations in the polynomial coefficients as the order of the polynomial gets large, and order 9 is a bit high. Are you sure gamma and the other parameters affecting the coefficients are accurately given, to the maximum precision possible, compared to the original paper? In particular, does gamma really only have 3 significant digits?
Also, instead of,
om=om_data(ii);
it would be more accurate to have,
om=0.01+ii*0.001;
6 个评论
Matt J
2020-12-15
编辑:Matt J
2020-12-15
My best guess is that the paper only published their parameters (e.g., gamma) to 4 decimal places, whereas more precision is needed to obtain ttheir actual plots. Do you have any way of regenerating the input parameters from first principles? Otherwise, maybe contact the authors.
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