PeRK4plotter.java

Printed by Domenico Galli
Feb 14, 03 14:27
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PeRK4plotter.java
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//*****************************************************************************
// $Log: PeRK4plotter.java,v $
// Revision 1.2 2003/02/14 01:04:33 galli
// − bug fixed
// Revision 1.1 2003/02/14 00:59:50 galli
// − Initial revision
//*****************************************************************************
// pendolo semplice
// punto materiale vincolato a una circonferenza giacente su di un piano
//
verticale
// usa il metodo di Runge−Kutta del IV ordine
// traccia i grafici dei risultati
//*****************************************************************************
import java.io.*;
import java.util.*;
import java.awt.*;
import java.awt.geom.*;
//*****************************************************************************
public class PeRK4plotter
{
double l;
double g=9.80665;
double x0,v0;
double t,x,v,a;
double tMax,deltaT;
java.util.List lxt,lvt,lat;
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
public static void main(String args[])
{
PeRK4plotter peRK4plotter=new PeRK4plotter();
peRK4plotter.dataRead();
peRK4plotter.run();
peRK4plotter.plot();
}
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
// creatore
PeRK4plotter()
{
lxt=new ArrayList();
lvt=new ArrayList();
lat=new ArrayList();
}
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
// legge i dati iniziali da console
void dataRead()
{
BufferedReader stdin=new BufferedReader(new InputStreamReader(System.in));
try
{
System.out.print("lunghezza=m ");
l=Double.parseDouble(stdin.readLine());
System.out.print("phi0=gradi ");
x0=Math.PI/180.0*Double.parseDouble(stdin.readLine());
System.out.print("omega0=gradi/s ");
v0=Math.PI/180.0*Double.parseDouble(stdin.readLine());
System.out.print("tMax=s ");
tMax=Double.parseDouble(stdin.readLine());
System.out.print("deltaT=s ");
deltaT=Double.parseDouble(stdin.readLine());
}
catch(IOException ioe)
{
System.out.println(ioe);
System.exit(1);
}
catch(NumberFormatException nfe)
{
System.out.println(nfe);
System.exit(1);
}
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Printed by Domenico Galli
Feb 14, 03 14:27
PeRK4plotter.java
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System.out.println("l="+l+", phi0="+x0+", omega0="+v0+", tMax="+tMax+
", deltaT="+deltaT);
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}
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
// esegue il calcolo
void run()
{
int i;
double xpg;
double k1,j1,k2,j2,k3,j3,k4,j4,vm1,am1,vm2,am2,vf,af;
// storePeriod=periodo di disegno dati sul grafico
// Disegna 1 punto ogni storePeriod dati
// Disegna al massimo 10000 punti
int storePeriod=Math.max(1,(int)(tMax/deltaT)/10000);
x=x0;
v=v0;
a=−g*Math.sin(x)/l;
// accelerazione iniziale
lxt.add(new Point2D.Float((float)0,(float)(180.0*x0/Math.PI)));
lvt.add(new Point2D.Float((float)0,(float)(180.0*v0/Math.PI)));
lat.add(new Point2D.Float((float)0,(float)(180.0*a/Math.PI)));
for(t=0.0,i=0;;)
{
// algoritmo di Runge−Kutta IV ordine
k1=v*deltaT;
j1=a*deltaT;
vm1=v+j1/2;
am1=−g*Math.sin(x+k1/2)/l;
k2=vm1*deltaT;
j2=am1*deltaT;
vm2=v+j2/2;
am2=−g*Math.sin(x+k2/2)/l;
k3=vm2*deltaT;
j3=am2*deltaT;
vf=v+j3;
af=−g*Math.sin(x+k3)/l;
k4=vf*deltaT;
j4=af*deltaT;
x=x+(k1+2*k2+2*k3+k4)/6;
v=v+(j1+2*j2+2*j3+j4)/6;
a=−g*Math.sin(x)/l;
// fine algoritmo di Runge−Kutta IV ordine
// xpg=angolo nel primo giro. −PI<xpg<PI
xpg=x−2*Math.PI*Math.floor((x+Math.PI)/(2*Math.PI));
t=t+deltaT;
i++;
if(t>tMax)break;
// se ci sono > 10000 punti, memorizza 1 punto ogni storePeriod punti
if(i%storePeriod==0)
{
lxt.add(new Point2D.Float((float)t,(float)(180.0*xpg/Math.PI)));
lvt.add(new Point2D.Float((float)t,(float)(180.0*v/Math.PI)));
lat.add(new Point2D.Float((float)t,(float)(180.0*a/Math.PI)));
System.out.println(i+"\tt="+t+"\tx="+xpg+"\tv="+v+"\ta="+a);
}
}
}
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
// disegna il grafico
void plot()
{
Plot2D2M pP0=new Plot2D2M(700,400);
pP0.setPlotColor(Color.red);
pP0.setXunits("s");
pP0.setYunits("gradi");
pP0.setXmin(0);
pP0.resizeForVals(lxt);
pP0.drawAxes();
pP0.drawPoints(lxt);
pP0.drawPolyLine(lxt);
PlotFrame pF0=new PlotFrame();
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Feb 14, 03 14:27
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pF0.setTitle("Spostamento angolare");
pF0.setLocation(new Point(20,20));
pF0.getContentPane().add(pP0,BorderLayout.CENTER);
pF0.pack();
pF0.setVisible(true);
//.........................................................................
Plot2D2M pP1=new Plot2D2M(700,400);
pP1.setPlotColor(Color.magenta);
pP1.setXunits("s");
pP1.setYunits("gradi/s");
pP1.setXmin(0);
pP1.resizeForVals(lvt);
pP1.drawAxes();
pP1.drawPoints(lvt);
pP1.drawPolyLine(lvt);
PlotFrame pF1=new PlotFrame();
pF1.setTitle("Velocità angolare");
pF1.setLocation(new Point(40,40));
pF1.getContentPane().add(pP1,BorderLayout.CENTER);
pF1.pack();
pF1.setVisible(true);
//.........................................................................
Plot2D2M pP2=new Plot2D2M(700,400);
pP2.setPlotColor(Color.blue);
pP2.setXunits("s");
pP2.setYunits("gradi/s²");
pP2.setXmin(0);
pP2.resizeForVals(lat);
pP2.drawAxes();
pP2.drawPoints(lat);
pP2.drawPolyLine(lat);
PlotFrame pF2=new PlotFrame();
pF2.setTitle("Accelerazione angolare");
pF2.setLocation(new Point(60,60));
pF2.getContentPane().add(pP2,BorderLayout.CENTER);
pF2.pack();
pF2.setVisible(true);
}
//−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−
180
}
//*****************************************************************************
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