MATLAB: Small “toy rocket” – Simulation

MATLAB

 I'm trying to simulate a "toy rocket" launch and I want to get the plots of height-time and velocity-time. I've used the code below to simulate the timeperiod 0-0.15 seconds but it takes forever to plot the whole code (step1,step2,step3). Instead I would like to save the loop-data in a array/matrix and plot all the steps later on in the code. How can I succeed with this?
  • Functions*
function [a] = acceleration(F,m,g)
a=(F-m*g)/m;
function [v] = velocity(a,t,v0,t0)
v=v0+a*(t-t0);
function [h] = height(a,t,h0,v0,t0)
h=h0+v0*(t-t0)+(1/2)*a*(t-t0)^2;
Code starts:
        v0=0; %Initial velocity
        h0=0; %Initial height
        t0=0; %Initial time
        g=9.81; %The gravitational constant
        %Input variables
        F=input('Engine force (N): ');
        m=input('Mass (kg): ');
        dt=input('Precision/timesteps (s): ');
        %Step one
        hold on
        for t = t0: dt: 0.15 
          velocity1=velocity(acceleration(F,m,g),t,v0,t0);
         height1=height(acceleration(F,m,g),t,h0,v0,t0);
          plot(t,height1);
          h=plot(t,velocity1);
          set(h,'Color','r');
        end

Best Answer

You're super close...
Just make one change to the height function so it looks like this one below:
function [h] = height(a,t,h0,v0,t0)
    h=h0+v0*(t-t0)+(1/2)*a*(t-t0).^2;
end
(Notice the .^ instead of ^ to signify element-wise exponentiation. This way you can pass entire vectors in place of t.)
Then, modify the main code by remove the for-loop and instead use something like
    v0=0; %Initial velocity
    h0=0; %Initial height
    t0=0; %Initial time
    g=9.81; %The gravitational constant        %Input variables
    F=input('Engine force (N): ');
    m=input('Mass (kg): ');
    dt=input('Precision/timesteps (s): ');        %Step one       
    t = t0: dt: 0.15;
    velocity1=velocity(acceleration(F,m,g),t,v0,t0);
    height1=height(acceleration(F,m,g),t,h0,v0,t0);
    plot(t,height1,'b',t,velocity1,'r');
Notice that t is now a vector and that I'm only calling the plot function once, the first curve (height vs. t) is blue ('b') and the second curve (velcoity1 vs t) is red. Hopefully that helps.
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