Ode45 calling a matrix and an array in a function

%question 7

ts = [0,1,2,3];

q = zeros(4,length(ts));

% q(1:4,1) = 0.5;

[t,q] = ode45(@(q,ts) q_dotf(q,ts), ts, q_b); %where q_b is [0.5,0.5,0.5,0.5] in early part of code

%and the function is

function q_dot = q_dotf(q,ts)

a = 0.2*cos(0.05*ts);

b = 0.2*sin(0.05*ts);

c = zeros(1,length(ts));

c(1,:) = 0.1;

d = zeros(1,length(ts));

w_bbif = [a;b;c;d];

I3 = eye(3);

q4 = q(4);

q_13 = q(1:3);

q_13x = [0 -q(3) q(2);

q(3), 0, -q(1);

-q(2), q(1), 0];

a1 = [(q4*I3+q_13x) q_13;

-q_13', q4];

q_dot = 1/2*(a1*w_bbif);

end

I do not understand why i keep getting errors such as w_bbif is not concatenated, and that q4 = q(4) produces aan index error. I am trying to produce a code that implements ode45 to produce q from q_dot. But errors seem to arise when trying to put matrices in function. Any help would be wonderful.

[VBBV]

Change this line

q = zeros(4,length(ts));

To

q = zeros(1,length(ts));

[Alex Belew]

has to be the 4xn matrix because of definition of quaternion otherwise I would do that. Thank you so much for the answer!

Answer 1

[Torsten]

Your arguments to q_dot are inverted:

Use

function q_dot = q_dotf(ts,q)

instead of

function q_dot = q_dotf(q,ts)

And note that ts in q_dot is not your original ts, but some value in between ts(1) and ts(end) depending on the progress of the integration.

ts = [0,1,2,3];
q_b(1:4,1) = 0.5;
[t,q] = ode45(@q_dotf, ts, q_b); 
plot(t,q(:,1))

function q_dot = q_dotf(ts,q)
  a = 0.2*cos(0.05*ts);
  b = 0.2*sin(0.05*ts);
  c = zeros(1,length(ts));
  c(1,:) = 0.1;
  d = zeros(1,length(ts));
  w_bbif = [a;b;c;d];
  I3 = eye(3);
  q4 = q(4);
  q_13 = q(1:3);
  q_13x = [0 -q(3) q(2);
           q(3), 0, -q(1);
          -q(2), q(1), 0];
  a1 = [(q4*I3+q_13x) q_13;
        -q_13', q4];
  q_dot = 1/2*(a1*w_bbif);
end

[Alex Belew]

Thank you so much for your answer, I do not know why I had to switch q and ts but it works wonderfully now!

[Torsten]

I do not know why I had to switch q and ts but it works wonderfully now!

Because ode45 transfers time at the first position and the values of your solution variables at the second position in the list of inputs. The names of the variables don't matter, of course.

So if you write your function as

function q_dot = q_dotf(q,ts)

then q is time and ts are your solution variables.