System of 2nd order ODE with Euler.
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Guillaume Theret
el 27 de Mayo de 2021
Comentada: Guillaume Theret
el 27 de Mayo de 2021
Hi,
I had a system of 2 2nd order ODE.
I got to this point :
I need to find the approximate solutions of y2(t).
M1, M2, G, L1,L2 are variables given by the user.
These are the initials conditions which are given by the user also(i guess ?)
Im a bit lost in what should i do. I know how euler works but not with this type of system.
thanks !
4 comentarios
Guillaume Theret
el 27 de Mayo de 2021
Editada: Guillaume Theret
el 27 de Mayo de 2021
Respuesta aceptada
Jan
el 27 de Mayo de 2021
Editada: Jan
el 27 de Mayo de 2021
You got it almost. I've fixed a typo and expanded the Euler method to collect the output as matrix.
% function main
xinit = 0;
xfinal = 3;
h = 0.05;
y0 = [1, 0, 0, 0]; % As many elements as the system has
[x, y] = euler_explicit(@fnc, xinit, xfinal, h, y0);
plot(x, y);
% end
function [x, y] = euler_explicit(f, xinit, xfinal, h, y0)
x = xinit : h : xfinal;
n = length(x);
y = zeros(n, numel(y0));
y(1, :) = y0;
for k = 1:n - 1
y(k + 1, :) = y(k, :) + h * f(x(k), y(k, :));
end
end
function dy = fnc(t,Y)
L1 = 1;
L2 = 2;
M1 = 2;
M2 = 3;
g = 1;
K = 1 / (L1 * L2 * (M1 + M2*sin(Y(1) - Y(2)).^2));
% ^ was missing
Y4 = K*((M1+M2)*g*L1*sin(Y(1))*cos(Y(1)-Y(2)) - (M1+M2)*g*L1*sin(Y(2)) + (M1+M2)*L1^2*sin(Y(1) - Y(2))*Y(3)^2 + M2*L1*L2*sin(Y(1)-Y(2))*cos(Y(1)-Y(2))*Y(4)^2);
Y3 = K*(-(M1+M2)*g*L2*sin(Y(1)) + M2*g*L2*sin(Y(2))*cos(Y(1)-Y(2)) - M2*L1*L2*sin(Y(1) - Y(2))*cos(Y(1)-Y(2))*Y(3)^2 - M2*L2^2*sin(Y(1)-Y(2))*Y(4)^2);
dy = [Y(3), Y(4), Y3, Y4];
end
Más respuestas (1)
Torsten
el 27 de Mayo de 2021
- y0 must be a 4x1 vector, not a scalar.
- ye = zeros(4,n) instead of ye=zeros(1,n)
- ye(:,1) = y0 instead of ye(1) = y0
- ye(:,i+1) = ye(:,i) + h*f(x(i),ye(:,i)) instead of the expression in your loop
- dy = [Y(3);Y(4);Y3;Y4] instead of the row vector in your code
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