Double Pendulum in C (Trace Motion Real-Time + gif output)?

In summary: ); s2 = th2_yder((t1d + (r1/2)), (th1 + (k1/2)), (t2d +(s1/2)), (th2 + (q1/2)), l1, l2, m1,...); printf("%f\t%f\t%f\t%f\n", x2, y2, x1, y1, k1, q1, r1, s1); printf("%f\t%f\t%f\t%f\n", x2, y2,
  • #1
billyp245
3
0
I have written a C program to trace out the motion of a double pendulum, but am having difficulties in getting gnuplot (controlled from my c program) to trace out the paths of the masses (example video below). Thus far I have created the program such that it produces a number of png images at each interval (using runge kutta method), however I want to output it as a gif instead so a line traces out the path of the masses in real time.



Been stuck for quite a while so any help is greatly appreciated! In the code below I am assuming the problem occurs with piping out to gnuplot from within the for loop (to save you from wasting your time sifting through it)

Code:
/* Header Files */
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <time.h>
#include <assert.h>

// Definitions
#define GRAVITY 9.8
#define INCREMENT 0.0175

// Declerations of functions
double th1_xder(double t1d);
double th1_yder(double t2d);
double th2_xder(double t1d, double th1, double t2d, double th2, double l1, double l2, double m1, double m2);
double th2_yder(double t1d, double th1, double t2d, double th2, double l1, double l2, double m1, double m2);

int main (int argc, char * argv[]) {

    double x1=0, y1=0, x2=0, y2=0; //coordinates
    double l1=0, l2=0;  //lengths
    double m1=0, m2=0;  //masses
    double th1=0, th2=0; //angles
    double t1d=0, t2d=0; //zero velocity initially

    //second order Runge-Kutta equations
    double k1=0, k2=0, k3=0, k4=0; //for x1
    double q1=0, q2=0, q3=0, q4=0; //for y1
    double r1=0, r2=0, r3=0, r4=0; //for x2
    double s1=0, s2=0, s3=0, s4=0; //for y2

    int i = 0;
    double x0=0, y0=0;

    printf("Enter '1' to input your own data or '0' to use the preset data\n");
    char dummy = 'a';
    scanf("%c", &dummy);
    assert((dummy == '1') || (dummy == '0'));

    if (dummy == '1') {

        printf("Please enter a length l1:\n");
        scanf("%lf", &l1);
        printf("Please enter a length l2:\n");
        scanf("%lf", &l2);
        printf("Please enter a mass m1:\n");
        scanf("%lf", &m1);
        printf("Please enter a mass m2:\n");
        scanf("%lf", &m2);
        printf("Please enter an angle theta1:\n");
        scanf("%lf", &th1);
        printf("Please enter an angle theta2:\n");
        scanf("%lf", &th2);
    } else {

        l1 = 1;
        l2 = 1;
        m1 = 1;
        m2 = 1;
        th1= 90;
        th2= 0;
    }

    th1 = th1*(M_PI/180);
    th2 = th2*(M_PI/180); 

    FILE *fsp;

    if((fsp=fopen("origin.dat", "w"))==NULL) {
        fprintf(stdout, "cannot open origin.dat\n");
        exit (EXIT_FAILURE);
    }

    fprintf(fsp, "0\t0");
        fclose(fsp); 

    FILE *fout;

    if((fout=fopen("testout.dat", "w"))==NULL) {
        fprintf(stdout, "cannot open testout.dat\n");
        exit (EXIT_FAILURE);
    }

    printf("%f\t%f\t%f\t%f\n", x1, y1, x2, y2); 
    fprintf(fout, "%f\t%f\t%f\t%f\n", x1, y1, x2, y2);

    for(i = 0; i < 250; i++) {

        if ((fout=fopen("testout.dat", "w"))==NULL) {
            fprintf(stdout, "cannot open testout.dat\n");
            exit (EXIT_FAILURE);
        }

        k1 = th1_xder(t1d);
        q1 = th1_yder(t2d);
        r1 = th2_xder(t1d, th1, t2d, th2, l1, l2, m1, m2);
        s1 = th2_yder(t1d, th1, t2d, th2, l1, l2, m1, m2);

        k2 = th1_xder(t1d + (r1/2));
        q2 = th1_yder(t2d + (s1/2));
        r2 = th2_xder((t1d + (r1/2)), (th1 + (k1/2)), (t2d +(s1/2)), (th2 + (q1/2)), l1, l2, m1, m2);
        s2 = th2_yder((t1d + (r1/2)), (th1 + (k1/2)), (t2d +(s1/2)), (th2 + (q1/2)), l1, l2, m1, m2);

        k3 = th1_xder(t1d + (r2/2));
        q3 = th1_yder(t2d + (s2/2));
        r3 = th2_xder((t1d + (r2/2)), (th1 + (k2/2)), (t2d +(s2/2)), (th2 + (q2/2)), l1, l2, m1, m2);
        s3 = th2_yder((t1d + (r2/2)), (th1 + (k2/2)), (t2d +(s2/2)), (th2 + (q2/2)), l1, l2, m1, m2); 

        k4 = th1_xder(t1d + r3);
        q4 = th1_yder(t2d + s3);
        r4 = th2_xder((t1d + r3), (th1 + k3), (t2d + s3), (th2 + q3), l1, l2, m1, m2);
        s4 = th2_yder((t1d + r3), (th1 + k3), (t2d + s3), (th2 + q3), l1, l2, m1, m2);

        t1d = t1d + (r1 + 2*r2 + 2*r3 + r4)/6;
        t2d = t2d + (s1 + 2*s2 + 2*s3 + s4)/6;
        th1 = th1 + (k1 + 2*k2 + 2*k3 + k4)/6;
        th2 = th2 + (q1 + 2*q2 + 2*q3 + q4)/6;

        x1 = l1*sin(th1);
        y1 = -l1*cos(th1);
        x2 = x1 + l2*sin(th2);
        y2 = y1 - l2*cos(th2);

        printf("%f\t%f\t%f\t%f\n", x1, y1, x2, y2); 
        fprintf(fout, "%f\t%f\t%f\t%f\n", x1, y1, x2, y2);

        fclose(fout);

        FILE *gnuplotPipe = popen("gnuplot -persist","w");
        if (gnuplotPipe) {
            fprintf(gnuplotPipe, "set style data lines\n");
            fprintf(gnuplotPipe, "set terminal png nocrop enhanced size 1280,720; set output 'yyy%d.png'\n", i);
            fprintf(gnuplotPipe, "set title 'frame%d'\n", i);
            fprintf(gnuplotPipe, "set multiplot\n");
            fprintf(gnuplotPipe, "set xrange [-2.5:2.5]; set yrange [-2.5:2]\n");
            fprintf(gnuplotPipe, "unset key; unset ytics; unset xtics\n");                  
            fprintf(gnuplotPipe, "plot 'testout.dat' using 3:4\n");
            fprintf(gnuplotPipe, "plot '-' with lines lw 2 lc rgb 'black', 'testout.dat' u 1:2 w points pt 7 ps 2, 'testout.dat' u 3:4 w points pt 7 ps 2, 'origin.dat' u 1:2 w points pt 7 ps 2 lc 0\n");
            fprintf(gnuplotPipe, "%f %f\n", x0, y0);
            fprintf(gnuplotPipe, "%f %f\n", x1, y1);
            fprintf(gnuplotPipe, "%f %f\n", x2, y2);
            fprintf(gnuplotPipe, "e\n");  
            fprintf(gnuplotPipe, "\n");
            fprintf(gnuplotPipe, "set nomultiplot\n");              
            fflush(gnuplotPipe);          
            fprintf(gnuplotPipe,"exit \n");
            pclose(gnuplotPipe);
        }                                        
    }             

    return EXIT_SUCCESS;
}

double th1_xder(double t1d) {

    double k = t1d*INCREMENT;
    return k;
}

double th1_yder(double t2d) {

    double m = t2d*INCREMENT;
    return m;
}

double th2_xder(double t1d, double th1, double t2d, double th2, double l1, double l2, double m1, double m2) {

    double l = INCREMENT*((GRAVITY/l1)*((m2/(m1 + m2))*sin(th2)*cos(th1-th2)-sin(th1))-(m2/(m1 + m2))*sin(th1-th2)*((l2/l1)*t2d*t2d + t1d*t1d*cos(th1-th2)))/(1-((m2/(m1 + m2))*cos(th1-th2)*cos(th1-th2)));
    return l;
}

double th2_yder(double t1d, double th1, double t2d, double th2, double l1, double l2, double m1, double m2) {

    double p = INCREMENT*((GRAVITY/l2)*(sin(th1)*cos(th1-th2)-sin(th1)) + sin(th1-th2)*((l1/l2)*t1d*t1d + (m2/(m1 + m2))*t2d*t2d*cos(th1-th2)))/(1-((m2/(m1 + m2))*cos(th1-th2)*cos(th1-th2)));
    return p;
}
 
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  • #2
Is popen() returning a valid pointer? If it's returning a null pointer or -1, the stream isn't valid.
 
  • #3
Thanks for the suggestion however the stream was valid. I didn't manage to get the tracing of the paths working (as in the above video) however I did get the output of the gif animation. I simply had to open the pipe into gnuplot outside of my loop, do the plotting inside the loop to create all the frames, and then close the pipe once the loop was finished. I had tried that earlier but hadn't placed the 'set multiplot' command outside the loop which was giving me the error.
 

FAQ: Double Pendulum in C (Trace Motion Real-Time + gif output)?

What is a double pendulum?

A double pendulum is a physical system consisting of two pendulums connected together at a common point. It is a chaotic system, meaning that its motion is highly sensitive to initial conditions and can be difficult to predict.

What is the significance of studying the double pendulum in C?

C is a high-level programming language commonly used in scientific research. By studying the double pendulum in C, scientists can model and analyze its complex behavior in real-time, allowing for a better understanding of chaotic systems and their applications.

How does the trace motion real-time feature work?

The trace motion real-time feature in a double pendulum simulation records the position of the pendulums at each time step and displays a continuous line tracing their movement. This allows for a visual representation of the pendulums' chaotic motion.

Can the C program output a gif of the double pendulum's motion?

Yes, the C program can be configured to output a gif of the double pendulum's motion. This can be useful for visualizing the pendulum's behavior and for sharing the results of the simulation with others.

What are the potential applications of studying the double pendulum in C?

Studying the double pendulum in C can have many potential applications, such as in physics research, engineering, and robotics. It can also be used as a teaching tool to demonstrate chaotic systems and their behavior.

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