MATLAB: System of 2nd order ODE with Euler.

euler

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 !

Best Answer

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
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