/*
 * h6a.java - revised 19 Apr 05 - width 433, height 361
 * @author jackord@kw.igs.net
 * central force motion: apsidal angle integral
 */

import java.applet.Applet;
import java.awt.*;
import java.awt.event.ActionListener;
import java.awt.event.ActionEvent;

public class h6a extends Applet
                   implements ActionListener {
  int kk=0; int norbit=1; int orbit=0;                 // Declarations
  double c=0; double dr=0;
  double [] dtheta=new double[1001];
  String b1s="-2"; Button b1=new Button(b1s);
  String b2s="-1"; Button b2=new Button(b2s);
  String b3s="+1"; Button b3=new Button(b3s);
  String b4s="Orbit"; Button b4=new Button(b4s);

  public void init() {
    setLayout(new FlowLayout(FlowLayout.LEFT));
    add(b1); add(b2); add(b3); add(b4);
    b1.addActionListener(this);
    b2.addActionListener(this);
    b3.addActionListener(this);
    b4.addActionListener(this);
    setBackground(new Color(211, 211, 211));
  }

  public void paint(Graphics g) {
    double a, b, cf, e, en, x, y, ya, yb, yc, l, l2;
    double r, theta, z1, z2;
    int x1, y1, x2, y2; int np=1000; cf=5;
    g.setFont(new Font("TimesRoman", Font.PLAIN, 14));
    g.setColor(Color.black); g.drawRect(0, 0, 432, 360);
    if (kk==2) {
      g.setColor(Color.green); g.fillArc(206, 170, 21, 21, 0, 360);
      g.setColor(Color.black); g.drawArc(206, 170, 20, 20, 0, 360);
      g.setColor(Color.red);                           
      g.drawArc(36, 0, 360, 360, 0, 360);
      x1=(int)(180*(1.2-c)); y1=(int)(180*(1-c));
      g.drawArc(x1, y1, (int)(2*c*180+.5), (int)(2*c*180+.5), 0, 360);
      g.setColor(Color.blue);
    }
    else {
      g.drawString("Force Law Power", 0, 45);
      g.drawLine(216, 180, 432, 180);
      g.drawLine(216, 0, 216, 360);
    }
    if (kk==2) {                                       // Plot Orbit
      r=1; theta=0; x1=396; y1=180;
      for (int j=1; j<=norbit; j=j+1) {
        for (int i=1; i<=np; i=i+1) {
          r=r-dr; theta=theta+dtheta[i];
          x2=(int)(180*(1.2+r*Math.cos(theta))); y2=(int)(180*(1-r*Math.sin(theta)));
          g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
        }
        for (int i=np; i>=1; i=i-1) {
          r=r+dr; theta=theta+dtheta[i];
          x2=(int)(180*(1.2+r*Math.cos(theta))); y2=(int)(180*(1-r*Math.sin(theta)));
          g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
        }
      }
      kk=0; orbit=0;
    }
    if (kk!=0) {
      g.setColor(Color.green);                         // Plot Energy Diagram
      l=.488; l2=l*l/2; x=1.2; y=l2/x/x; x1=432; y1=(int)(180*(1-y/cf));
      do {
        x=x-.002; y=l2/x/x;
        x2=(int)(180*(1.2+x)); y2=(int)(180*(1-y/cf));
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while (y<cf);
      g.setColor(Color.magenta);
      x=1.2; y=v(x); x1=432; y1=(int)(180*(1-y/cf));
      do {
        x=x-.002; y=v(x);
        x2=(int)(180*(1.2+x)); y2=(int)(180*(1-y/cf));
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while ((y>-cf)&&(x>0));
      g.setColor(Color.blue);
      x=1.2; y=l2/x/x+v(x); x1=432; y1=(int)(180*(1-y/cf));
      do {
        x=x-.002; y=l2/x/x+v(x);
        x2=(int)(180*(1.2+x)); y2=(int)(180*(1-y/cf));
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while (y<cf);
      g.setColor(Color.red);
      en=l2+v(1); y1=(int)(180*(1-en/cf)); g.drawLine(216, y1, 432, y1);
      e=1E-8; a=.1; b=.5; c=0;                         // Find Pericenter
      ya=l2/a/a+v(a); yb=l2/b/b+v(b); yc=0;
      while ((b-a)>e) {                                // Bisection Algorithm
        c=(a+b)/2; yc=l2/c/c+v(c);
        if (yc>en) {
          a=c;
        }
        else {
          b=c;
        }
      }
      x1=(int)(180*(1.2+c)); g.drawLine(x1, 180, x1, y1);
      g.drawLine(396, 180, 396, y1);                   // Show Apsides
      theta=0; z1=0; dr=(1-c)/np;                      // Find Apsidal Angle
      for (int i=1; i<np; i=i+1) {
        r=1-i*dr; z2=r*r/l*Math.sqrt(2*(en-l2/r/r-v(r)));
        dtheta[i]=2*dr/(z1+z2); theta=theta+dtheta[i]; z1=z2;
      }
      dtheta[np]=2*dr/z1; theta=theta+dtheta[np];
      g.drawString("Apsidal Angle", 0, 60);
      g.drawString(Float.toString((float)(theta*180/Math.PI))+" deg", 0, 75);
      kk=0; orbit=1;
    }
  }

  double v(double r) {                                 // Potential
    double y=0;
    if (kk==-2) {
      y=-1/r;
    }
    if (kk==-1) {
      y=Math.log(r);
    }
    if (kk==1) {
      y=r*r/2;
    }
    return y;
  }

  public void actionPerformed(ActionEvent e) {
    String tst;
    tst=e.getActionCommand();
    if (b1s.equals(tst)) { kk=-2; norbit=1; }
    if (b2s.equals(tst)) { kk=-1; norbit=16; }
    if (b3s.equals(tst)) { kk=1; norbit=2; }
    if (b4s.equals(tst)) { if (orbit==1) { kk=2; } }
    repaint();
  }
}