# Small "toy rocket" - Simulation

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fxo on 23 Apr 2013
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

Kye Taylor on 23 Apr 2013
Edited: Kye Taylor on 23 Apr 2013
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.
fxo on 24 Apr 2013
So then this code should be correct
t=t0:dt:0.15;
y=1:length(t);
for i = y
velocity1=velocity(acceleration(F,m,g),t,v0,t0);
height1=height(acceleration(F,m,g),t,h0,v0,t0);
end
It do seem to work so once again, thank you really appreciate it!

Damian Prashad on 28 Oct 2019
Cool project. Now I'd like to do the opposite and land a rocket. Can someone help me with the code? I'd like to use state space form given intial conditions.
Thank you,

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