### Example: Contour Chart from Gridded Data

In the restricted three-body problem, two large objects (masses and ) a distance a apart, undergoing mutual gravitational attraction, circle a common center-of-mass. A third small object (mass m ) is assumed to move in the same plane as and and is assumed to be two small to affect the large bodies. For simplicity, we use a coordinate system that has the center of mass at the origin. and are on the x -axis at and , respectively.

In the center-of-mass coordinate system, the effective potential energy of the system is given by

The universal gravitational constant is G . The following program plots the part of V(x,y) inside of the square bracket. The factor is ignored because it just scales the plot.

import com.imsl.chart.*;

public class ContourEx1 extends javax.swing.JApplet {

private JPanelChart panel;

public void init() {
Chart chart = new Chart(this);
panel = new JPanelChart(chart);
setup(chart);
}

static private void setup(Chart chart) {
int nx = 80;
int ny = 80;

// Allocate space
double xGrid[] = new double[nx];
double yGrid[] = new double[ny];
double zData[][] = new double[nx][ny];

// Setup the grids points
for (int i = 0; i < nx; i++) {
xGrid[i] = -2 + 4.0 * i / (double) (nx - 1);
}
for (int j = 0; j < ny; j++) {
yGrid[j] = -2 + 4.0 * j / (double) (ny - 1);
}

// Evaluate the function at the grid points
for (int i = 0; i < nx; i++) {
for (int j = 0; j < ny; j++) {
double x = xGrid[i];
double y = yGrid[j];
double rm = 0.5;
double x1 = rm / (1.0 + rm);
double x2 = x1 - 1.0;
double d1 = Math.sqrt((x - x1) * (x - x1) + y * y);
double d2 = Math.sqrt((x - x2) * (x - x2) + y * y);
zData[i][j] = x2 / d1 - x1 / d2 - 0.5 * (x * x + y * y);
}
}

// Create the contour chart, with user-specified levels and a legend
AxisXY axis = new AxisXY(chart);
double cLevel[] = {-7, -5.4, -3, -2.3, -2.1, -1.97,
-1.85, -1.74, -1.51, -1.39, -1};
Contour c = new Contour(axis, xGrid, yGrid, zData, cLevel);
c.getContourLegend().setPaint(true);
}

public static void main(String argv[]) {
JFrameChart frame = new JFrameChart();
ContourEx1.setup(frame.getChart());
frame.setVisible(true);
}
}