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Program to plot 3D trajectory?

  1. Oct 12, 2012 #1
    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!!
     
  2. jcsd
  3. Oct 13, 2012 #2

    LCKurtz

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    I would use Maple (since that's the one I have experience with) or something equivalent to it.
     
  4. Oct 13, 2012 #3

    jhae2.718

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    Gold Member

    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:
    [tex]
    \begin{align*}
    \ddot{r} &= r\dot{\theta}^2 - \frac{k}{m}(r-l) \\
    \ddot{\theta} &= -\frac{2\dot{r}\dot{\theta}}{r}
    \end{align*}
    [/tex]
    Code (Text):

    [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]);
     
    Code (Text):

    [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.
     
    Last edited: Oct 13, 2012
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