Program to plot 3D trajectory?

[Adoniram]

Howdy folks,

I have been given the opportunity to do some extra credit for my mechanics class. As an assignment, my prof would like to see a 3D trajectory plotted via a program (like Python).

My basic assignment is to plot the trajectory of a soccer ball after it has been kicked. I don't need help with the physics equations, but I need to know what programs I can use and if one is better than the other. No worries learning the coding language, I have a lot of experience with Java, vb script, etc...

Ideally, I'd like to use a program that has a simple 3D plot of trajectory, and it would be even better if I could save the results as an independent program. If not, no big deal. Also, it would be superb if I could put in switches in the graphical output for things like turning wind on and off, air resistance, etc... If not, I'm sure I can just write multiple programs for each instance.

Thanks!

 

[LCKurtz]

I would use Maple (since that's the one I have experience with) or something equivalent to it.

 

[jhae2.718]

MATLAB is generally the standard in the dynamics community. FreeMat and Octave are open source clones of MATLAB.

There is a plot3 command in MATLAB that will do what you want.

Here's an example MATLAB simulation of a mass attached to a spring that behaves as a pendulum; its equations of motion are:
$$\begin{align*} \ddot{r} &= r\dot{\theta}^2 - \frac{k}{m}(r-l) \\ \ddot{\theta} &= -\frac{2\dot{r}\dot{\theta}}{r} \end{align*}$$

[color=#408080][i]%% Example simulation of a dynamical system.[/i][/color]
r0 = 1;
l = 1;
rdot0 = [color=#008000]rand[/color](1,1);
theta0 = [color=#008000]rand[/color](1,1);
thetadot0 = [color=#008000]rand[/color](1,1);
x0 = [r0 theta0 rdot0 thetadot0][color=#666666]'[/color];

[t x] = ode45(@pendulum, [0 100], x0);

r = x(:, 1);
theta = x(:, 2);

x = r [color=#666666].*[/color] [color=#008000]sin[/color](theta);
y = r [color=#666666].*[/color] [color=#008000]cos[/color](theta);

plot(x, y, x(1), y(1), [color=#BA2121]'+g'[/color], x([color=#008000][b]end[/b][/color]), y([color=#008000][b]end[/b][/color]), [color=#BA2121]'xr'[/color], [color=#BA2121]'MarkerFaceColor'[/color], [color=#BA2121]'r'[/color], [color=#BA2121]'linewidth'[/color], 3);
    tl = title([color=#BA2121]'X-Y Position of Spring-Mass Pendulum'[/color]);
    xl = xlabel([color=#BA2121]'x'[/color]);
    yl = ylabel([color=#BA2121]'y'[/color]);
    set([tl xl yl], [color=#BA2121]'fontsize'[/color], 16);
    legend([color=#BA2121]'Path'[/color], [color=#BA2121]'Start'[/color], [color=#BA2121]'End'[/color], [color=#BA2121]'Location'[/color], [color=#BA2121]'NorthEastOutside'[/color]);

[color=#008000][b]function[/b][/color][color=#bbbbbb] [/color] xdot =[color=#bbbbbb] [/color][color=#0000FF] pendulum[/color](t, x)[color=#bbbbbb]
    [/color]m = 1;
    k = 1;
    l = 1;

    r = x(1); theta = x(2); v = x(3); w = x(4);
    xdot = [v;
            w;
            r [color=#666666].*[/color] w[color=#666666].^[/color]2 [color=#666666]-[/color] k[color=#666666]/[/color]m [color=#666666]*[/color] (r [color=#666666]-[/color] l);
            [color=#666666]-[/color]2 [color=#666666]*[/color] v [color=#666666]*[/color] w [color=#666666]/[/color] r;
    ];
[color=#008000][b]end[/b][/color]

What you want to do will be much simpler than this, but this example should give you a taste of MATLAB.