MATLAB: Refresh plot for animation

animation

Hello

I would like to animate a pendulum rod with a mass attached through a spring. My question is about animation. Currently I am plotting the mass as a circle, and the rod as a line from origo to the endpoint. I use hold on, but this means I get every line in my animation. But If I do not use hold on it only plots the line and not the mass.

So how do I get a fresh image for every iteration of my loop?

Thanks in advance.

 for N = 2:1000
   hold on
   axis([-2*L1 2*L1 -2*L1 2*L1]);
   plot(bob_pos(1,N),bob_pos(2,N),'o', 'MarkerFaceColor', 'red');           %Plots the moving mass as circle
   plot([0 pend_end_pos(1,N)], [0 pend_end_pos(2,N)], '-');                 %Plots pendulum rod as line from origo to endpoint
   pause(0.025);
 end

Best Answer

Use the order

plot 1
hold on
plot 2
axis 
hold off 
drawnow()

... There are better ways than this but I am not at my desk at the moment

Related Solutions

MATLAB: Plot 3D lines along with slices

You can use HOLD to freeze the image and then add a line using the LINE command.

MATLAB: How to run the animation of double pendulum chaotic nature

Compare the results with the ODE45 integrator:

[T, Y] = ode45(F, [0, tmax], s(:, 1).');
figure;
plot(T, Y);
figure;
plot(s.')  % Your solution

The trajectories are similar, but not equal. This is a problem of the too large step width h=0.1. As soon as you reduce the step width to h=0.01 the results become nearly equal. Your Runge Kutta seems to be fine.

while t < tmax create the last time point 10.1, not 10.0. For a constant step width prefer:

t = linspace(0, 3, round(3 / 0.1) + 1);
s = zeros(4, numel(t));   % Pre-allocate!
for i = 2:numel(t)
  ...
end

Letting an array grow iteratively requires a lot of resources nd can reduce the runtime dramatically. Therefore a pre-allocation of the output is a good programming practice.

Start the loop at time point 2, because at t(1) the initial values are defined already. The wrong last time point is a small inaccuracy, but it can be avoided easily.

But you are right: I do not trust the trajectories also. If the integration is okay, the ODE must have a problem. How did you obtain it? Compare it with e.g. http://sophia.dtp.fmph.uniba.sk/~kovacik/doublePendulum.pdf. E.g. in the 4th component you have:

 ... - g*sin(s(2))*(m1+m2) / l2*(m1+m2)-m2*l2*cos(s(1)-s(2))^2

This means that only the last component of tne numerator is divided, so a parenthesis is missing:

( ... - g*sin(s(2))*(m1+m2) ) / l2*(m1+m2)-m2*l2*cos(s(1)-s(2))^2
^                           ^

For the first term of the 3rd component you have

-m2 * l1 * (s(4))^2 ...

but in the publication there is:

-m2 * l1 * (s(3))^2 ...

Writing this formula in a a large unreadable line as an anonymous function makes it hard to debug. Don't do this. Prefer a dedicated function, which allows to split the parts and check them using the debugger:

function dF = DoublePendulum(t, s, m1, m2, l1, l2, g)
s12 = s(1) - s(2);
m12 = m1 + m2;
n1 = -m2 * l1 * s(3)^2 * sin(s12) * cos(s12) + g * m2 * sin(s(2)) * cos(s12) - ...
   m2 * l2 * s(4)^2 * sin(s12) - m12 * g * sin(s(1));
d1 = l1 * m12 - m2 * l1 * cos(s12)^2;
n2 =  m2 * l2 * s(4)^2 * sin(s12) * cos(s12) + g * m12 * sin(s(1)) * cos(s12) + ...
   m12 * l1 * s(3)^2 * sin(s12) - m12 * g * sin(s(2));
d2 = l2 * m12 - m2 * l2 * cos(s12)^2;
dF = [s(3); ...
   s(4); ...
   n1 / d1, ...
   n2 / d2];
end

Now the pattern of the two equations is visible on first sight and finding typos like the s(3) or s(4) is much easier.

Then define in your code:

F = @(t,s) DoublePendulum(t, s, m1, m2, l1, l2, g);

By the way: It is a drawback to obtain the dependent X/Y coordinates befor the integeration. Integrating the formulas for the angles is much faster and more accurate. Then the results can be used easily to compute the karthesian coordinates afterwards for the visualization. For a double pendulum both will work, but if you simulate > 4 connected pendulums the computing time with dependent coordinates explodes and the accuracy degrades.

Best Answer

Related Solutions

MATLAB: Plot 3D lines along with slices

MATLAB: How to run the animation of double pendulum chaotic nature

Related Question