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/* -*-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 1.0/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;
}
picture(P(-6.5,-2.5), P(6.5, 8.5), "6.5 x 5.5in");
begin();
// calculate period, avoiding singularity at theta0
double period(4*(sqrt(2*EPS/(-Sin(theta0)))+Integral(f).eval(-theta0-EPS)));
border(Black(0.1), "1pt");
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-ell*P(x_t, y_t));
red();
ode_plot(F, posn0, period, 120);
blue();
box(posn);
box(pivot-ell*P(x_t, y_t));
end();
}
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