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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 !

Jan
on 27 May 2021

Edited: Jan
on 27 May 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

Torsten
on 27 May 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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