Simulation Toolkit (SmTk)

This example interactively solves damped simple harmonic oscillator. A damped simple harmonic oscillator can be written as two first order ordinary differatial equations (ODEs).

#include <math.h>
#include <smtk.h>
#include <smtk/rk4.h>
#include <smtk/plotter_2d.h>

static const double pi = 3.1415926535897932385;
static const double num_pi = 4.0; // size of X region plus a little.
                                  // This should be a multiple of 2.
static const double xmin = -2.0,
                    xmax = xmin + num_pi; // X region (xmin, xmax]
static const double b = 0.1;           // parameter: damping constant
static const double k = sqrt(2);
static double       x[2]; // position (angular position), velocity (angular velocity)
static double       t;    // time

static void difeq(double *xdot, const double *x, double t)
{
  xdot[0] = k * x[1];
  xdot[1] = - sin(pi*x[0]) - b * x[1];
}

static smtk::rk4<double,double,double>
rk4(difeq, /* differential equations call-back function */
    2,     /* 2 equations */
    0.04   /* time step */);

static double *init(double x_in, double y_in, bool &do_draw)
{
  x[0] = x_in; // position
  x[1] = y_in; // velocity
  t = 0.0;  // time

  if(x[0] > xmax || x[0] <= xmin)
    {
      while(x[0] > xmax)
        x[0] -= 2*pi;

      while(x[0] <= xmin)
        x[0] += 2*pi;
    }

  return x;
}

static double *step(bool &do_draw, bool &show_line)
{
  rk4.go(x, &t);

  // Map the position back into the region (-pi, pi] or (-1,1] with
  // the position defined by angle/pi.  If it jumps more than 2 (2 pi)
  // then you've got bigger problems than this remapping.

  if(x[0] > xmax || x[0] <= xmin)
    {
      show_line = false;
      if(x[0] > xmax)
        x[0] -= num_pi;
      else if(x[0] <= xmin)
        x[0] += num_pi;
    }

  // usleep slows this down.  Remove/add this to speed/slow it up.
  //usleep(10000);

  return x;
}

int main(void)
{
  smtk::plotter_2d plotter;

  plotter.
    set_window_title("Damped Pendulum").
    set_callbacks(1, init, step).
    set_line_width(3).
    set_point_width(2).
    set_scale(xmin+0.2, xmax-0.2, -2.1, 2.1).
    run();

  return 0;
}

Reference	Tutorial	Example Code
smtk::plotter_2d	interactive phase space plotter	damped_SHO.cpp damped_pendulum.cpp lotka_volterra.cpp multi_plot.cpp

doc/examples/by_class/plotter_2d/damped_SHO.cpp File Reference

Detailed Description