pendulum.flx

/* -*-flix-*- */
#include "epix.h"
using namespace ePiX;

P F(double u, double v)
{
  return P(v, -Sin(u));
}

double theta0=-5*M_PI/6;
double EPS=0.01; // to avoid singularity of f at theta0

P posn0(theta0, 0);

P pivot(0,5.5);
double ell=3;

double K=-Cos(theta0);

double f(double t)
{
  return recip(sqrt(2*(K+Cos(t))));
}

int main(int argc, char* argv[])
{
  if (argc == 3)
    {
      char* arg;
      double temp1, temp2;
      temp1=strtod(argv[1], &arg);
      temp2=strtod(argv[2], &arg);

      tix=temp1/temp2;
    }
  bounding_box(P(-2*M_PI,-1),P(2*M_PI,ell+pivot.x2()));
  unitlength("0.5in");
  picture(4*M_PI, 1+ell+pivot.x2());

  begin();

  // calculate period, avoiding singularity at theta0
  double period=4*(sqrt(2*EPS/(-Sin(theta0)))+I(f).eval(-theta0-EPS));

  rgb(0.95,0.95,0.95);
  grid();
  black();

  P posn=flow(F, posn0, period*tix, 120*tix); // phase position
  double x_t = -Sin(posn.x1());
  double y_t =  Cos(posn.x1());

  slope_field(F, P(-2*M_PI,-2), P(2*M_PI,2), 48, 12);

  bold();
  line(pivot, pivot-3*P(x_t, y_t));

  red();
  ode_plot(F, posn0, period, 120);

  blue();
  box(posn);
  box(pivot-3*P(x_t, y_t));

  end();
}