Solving Projectile Motion Problem Using ODE Solvers in MATLAB

[jcsolis]

Hello guys, I will work next summer session doing research with a professor and he asked me to do a couple of MATLAB problems using ODE solvers so I can get more familiar since I will be using it. One of the problems is about an object following a projectile motion and I need to solve it using ode15s and then plot the trajectory of the object.

Homework Statement

The given data for the object mass, initial velocity, angle, and gravity
m = 0.25 kg
v0 = 10 m/s
alpha = 45 degrees
g = 9.81 m/s^2

Homework Equations

The system of first order ODEs is the following

y'1= y2
y'2 = 0
y'3 = y4
y'4 = -g/m

Initial Conditions

y1(0) = 0
y2(0) = 0
y3(0) = Vo Cos(alpha)
y4(0) = Vo Sin (alpha)

Attempted Solution

Here is my M-File

function ydot = exercise1(t,y)
ydot = zeros(4,1);
ydot(1) = y(2);
ydot(2) = 0;
ydot(3) = y(4);
ydot(4) = -g/m;


Then on the command window I set up the given data
>> m = 0.25;
g = 9.81;
v = 10;
alpha = pi/4;
a = v*cos(alpha);
b = v*sin(alpha);

I run the program using ode15s and here is the result:

>> [T Y] = ode15s(@exercise1, [0 15], [0 a 0 b])

T =

0
0.0002
0.0004
0.0005
0.0018
0.0030
0.0042
0.0055
0.0161
0.0266
0.0372
0.0478
0.1536
0.2594
0.3653
0.4711
1.5293
2.5876
3.6458
4.7040
6.2040
7.7040
9.2040
10.7040
12.2040
13.7040
15.0000


Y =

1.0e+003 *

0 0.0071 0 0.0071
0.0000 0.0071 0.0000 0.0071
0.0000 0.0071 0.0000 0.0071
0.0000 0.0071 0.0000 0.0070
0.0000 0.0071 0.0000 0.0070
0.0000 0.0071 0.0000 0.0070
0.0000 0.0071 0.0000 0.0069
0.0000 0.0071 0.0000 0.0069
0.0001 0.0071 0.0001 0.0064
0.0002 0.0071 0.0002 0.0060
0.0003 0.0071 0.0002 0.0056
0.0003 0.0071 0.0003 0.0052
0.0011 0.0071 0.0006 0.0010
0.0018 0.0071 0.0005 -0.0031
0.0026 0.0071 -0.0000 -0.0073
0.0033 0.0071 -0.0010 -0.0114
0.0108 0.0071 -0.0351 -0.0529
0.0183 0.0071 -0.1131 -0.0945
0.0258 0.0071 -0.2350 -0.1360
0.0333 0.0071 -0.4009 -0.1775
0.0439 0.0071 -0.7113 -0.2364
0.0545 0.0071 -1.1100 -0.2952
0.0651 0.0071 -1.5970 -0.3541
0.0757 0.0071 -2.1723 -0.4130
0.0863 0.0071 -2.8359 -0.4718
0.0969 0.0071 -3.5877 -0.5307
0.1061 0.0071 -4.3084 -0.5815

I plotted the y versus x

>> plot(Y(:,1),Y(:,3))

the plot is attached so you can see the result, it is supposedly to look as a projectile path but my plot looks like a projectile going all the way down.

if someone can help me to see what I am doing wrong I would be really appreciated

Thank You guys

 

[jamesrc]

It looks like everything is okay except for your acceleration value - why is your equation for acceleration -g/m?

If you look at your data, you will see that the object does move up before it goes down as it should. You have a typo in your 'Relevant Equations' section (what you have for y(3) should be under y(2)) but it appears you did that part correctly when you retyped it later on.

Also, fyi, you can use the 'axis equal' command to rescale the graph which may be appropriate for this exercise (both the x and y axes are in meters).