/*
 * h6a.java - revised 24 Nov 2010 - width 433, height 401
 * @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 n=1; int norbit=1; int orbit=0;        // Global variables
  double c=0; double dr=0; double el=1;
  double [] dtheta=new double[10001];
  String b1s="+1"; Button b1=new Button(b1s);
  String b2s="0"; Button b2=new Button(b2s);
  String b3s="-1"; Button b3=new Button(b3s);
  String b4s="-2"; Button b4=new Button(b4s);
  String b5s="-3"; Button b5=new Button(b5s);
  String b6s="-5"; Button b6=new Button(b6s);
  String b7s="Orbit"; Button b7=new Button(b7s);

  public void init() {
    setLayout(new FlowLayout(FlowLayout.LEFT));
    add(b1); add(b2); add(b3); add(b4); add(b5); add(b6); add(b7);
    b1.addActionListener(this);
    b2.addActionListener(this);
    b3.addActionListener(this);
    b4.addActionListener(this);
    b5.addActionListener(this);
    b6.addActionListener(this);
    b7.addActionListener(this);
    setBackground(new Color(211, 211, 211));
  }

  public void paint(Graphics g) {
    double a, b, cf, e, en, x, y, ya, yb, yc, el2;
    double r, theta, z1, z2;
    int ro, xo, yo, x1, y1, x2, y2;
    xo=216; yo=200; ro=180; int np=10000; cf=5;
    g.setFont(new Font("TimesRoman", Font.PLAIN, 14));
    g.setColor(Color.black); g.drawRect(0, 0, 2*xo, 2*yo);
    if (kk==1) {
      g.drawLine(xo, yo, 2*xo, yo);                    // Axes for energy plot
      g.drawLine(xo, 0, xo, 2*yo);
      g.setColor(Color.green);                         // Plot Energy Diagram
      el2=el*el/2; x=1.2; y=el2/x/x; x1=2*xo; y1=(int)(yo-ro*y/cf);
      do {
        x=x-.002; y=el2/x/x;                           // Centrifugal potential
        x2=(int)(xo+ro*x); y2=(int)(yo-ro*y/cf);
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while (y2>0);
      g.setColor(Color.magenta);
      x=1.2; y=v(x); x1=2*xo; y1=(int)(yo-ro*y/cf);    // Central-force potential
      do {
        x=x-.002; y=v(x);
        x2=(int)(xo+ro*x); y2=(int)(yo-ro*y/cf);
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while ((y2<2*yo)&&(x2>xo));
      g.setColor(Color.blue);
      x=1.2; y=el2/x/x+v(x); x1=2*xo; y1=(int)(yo-ro*y/cf);
      do {
        x=x-.002; y=el2/x/x+v(x);                      // Total potential
        x2=(int)(xo+ro*x); y2=(int)(yo-ro*y/cf);
        g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
      } while ((y2<2*yo)&&(y2>0));
      g.setColor(Color.red);
      en=el2+v(1); y1=(int)(yo-ro*en/cf); g.drawLine(xo, y1, 2*xo, y1);
      if (n>-2.5) {
        e=1E-8; a=.1; b=.5; c=0;                       // Find Pericenter
        ya=el2/a/a+v(a); yb=el2/b/b+v(b); yc=0;
        while ((b-a)>e) {                              // Bisection Algorithm
          c=(a+b)/2; yc=el2/c/c+v(c);
          if (yc>en) {
            a=c;
          }
          else {
            b=c;
          }
        }
      }
      else {
        c=.1;                                          // Cutoff for -3 & -5
      }
      x1=(int)(xo+ro*c); g.drawLine(x1, yo, x1, y1);
      g.drawLine(xo+ro, yo, xo+ro, 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/el*Math.sqrt(2*(en-el2/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.setColor(Color.black);
      g.drawString("Force Law Power = "+n, 10, 50);
      if (n>-2.5) {
        g.drawString("Apsidal Angle "+(float)(theta*180/Math.PI)+" deg", 10, 70);
      }
      if (n==-3) { g.drawString("Spirals Toward Force Centre", 10, 70); }
      if (n==-5) { g.drawString("Circle Through Force Centre", 10, 70); }
      orbit=1;
    }
    if (kk==2) {                                       // Prep orbit plot
      g.setColor(Color.green); g.fillArc(xo-18, yo-18, 37, 37, 0, 360);
      g.setColor(Color.black); g.drawArc(xo-18, yo-18, 36, 36, 0, 360);
      g.setColor(Color.red);                           
      g.drawArc(xo-ro, yo-ro, 2*ro, 2*ro, 0, 360);     // Outer t.p. boundary
      if (n>-2.5) {
        x1=(int)(c*ro+.5);                            
        g.drawArc(xo-x1, yo-x1, 2*x1, 2*x1, 0, 360);   // Inner t.p. boundary
      }
      g.setColor(Color.blue);
      r=1; theta=0; x1=xo+ro; y1=yo;
      for (int j=1; j<=norbit; j=j+1) {
        for (int i=1; i<=np; i=i+1) {                  // In to inner t.p.
          r=r-dr; theta=theta+dtheta[i];
          x2=(int)(xo+ro*r*Math.cos(theta)); y2=(int)(yo-ro*r*Math.sin(theta));
          g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
        }
        if (n>-2.5) {
          for (int i=np; i>=1; i=i-1) {                // Back to outer t.p.
            r=r+dr; theta=theta+dtheta[i];
            x2=(int)(xo+ro*r*Math.cos(theta)); y2=(int)(yo-ro*r*Math.sin(theta));
            g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
          }
        }
        if (n==-5) {                                   // Lower half of circle
          r=1; theta=0; x1=xo+ro; y1=yo;
          for (int i=1; i<=np; i=i+1) {
            r=r-dr; theta=theta-dtheta[i];
            x2=(int)(xo+ro*r*Math.cos(theta)); y2=(int)(yo-ro*r*Math.sin(theta));
            g.drawLine(x1, y1, x2, y2); x1=x2; y1=y2;
          }
        }  
      }
      orbit=0;
    }
    kk=0;
  }

  double v(double r) {                                 // Potential
    double y=0;
    if (n==1) { y=r*r/2; }
    if (n==0) { y=r; }
    if (n==-1) { y=Math.log(r); }
    if (n==-2) { y=-1/r; }
    if (n==-3) { y=-1/r/r/2; }
    if (n==-5) { y=-1/r/r/r/r/4; }
    return y;
  }

  public void actionPerformed(ActionEvent e) {
    String tst;
    tst=e.getActionCommand();
    if (b1s.equals(tst)) { kk=1; n=1; norbit=2; el=.488; }
    if (b2s.equals(tst)) { kk=1; n=0; norbit=16; el=.488; }
    if (b3s.equals(tst)) { kk=1; n=-1; norbit=16; el=.488; }
    if (b4s.equals(tst)) { kk=1; n=-2; norbit=1; el=.488; }
    if (b5s.equals(tst)) { kk=1; n=-3; norbit=1; el=.999; }
    if (b6s.equals(tst)) { kk=1; n=-5; norbit=1; el=1/Math.sqrt(2); }
    if (b7s.equals(tst)) { if (orbit==1) { kk=2; } }
    repaint();
  }
}