/*** Integrates the pendlum using Euler method    ***/
/*** Rechnergestütztes Wissenschaftliches Rechnen ***/
/*** University of Goettingen, Germany 2004       ***/

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

double f1(double t, double phi, double omega)
{
  return(omega);
}

double f2(double t, double phi, double omega)
{
  return(-sin(phi));
}

int main(int argc, char **argv)
{
  double phi, omega;                    /* phase space variables */
  double phi_new, omega_new;           /* variables at next step */
  double h;                                          /* stepsize */
  int n, n_max;                            /* step, maximum step */
  double t;                                              /* time */

  sscanf(argv[1], "%lf", &h);       /* first argument = stepsize */
  sscanf(argv[2], "%d", &n_max); /*2nd argument = numb. of steps */
  phi=0; omega=1.0; t = 0;

  for(n=1; n<=n_max; n++)              /* iterate over all times */
  {
    printf("%f %f %f\n", t, phi, omega);        /* print results */
    phi_new = phi + h*f1(t,phi,omega);                /* integrate */
    omega_new = omega + h*f2(t,phi,omega);
    t += h;
    phi = phi_new; omega = omega_new;
  }
  return(0);
}