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Up: 3-Body Problem Configuration Simulator Previous: The Chenciner-Montgomery Figure-Eight

Using the Java Applet

The Java applet ThreeBodyApp contains two main panels: on the left is a depiction of the orbit of the bodies in their plane. The fixed origin of the applet appears as a small $\times$, while the center of mass of the configuration is drawn as $+$. Red lines depict the velocity vectors of the bodies, and the planets leave tracers behind them as they evolve. Both velocity vectors and tracers can be enabled or disabled by their checkboxes at the top of the window.

By default the center of the left frame will be focused on the center of mass of the system. Choosing from the drop-down list at the top of the window can refocus the point of view on either the mathematical origin of the internal coordinate system, or any of the three bodies. (The blue body is named Earth, yellow the Sun, and grey the Moon.)

When the animation is not running, you may click and drag the planets to reposition them in the frame, or click and drag the tips of the velocity vectors to change their velocities.

On the right is a depiction of the shape sphere. A small circle shows the projection of the current configuration, and as the system evolves the trajectory on the shape sphere is traced out. Darker colors indicate regions of the sphere which are further ``into the screen'' (i.e. down the $z$-axis) than lighter colors. The five central configurations $L_+, L_-, E_1, E_2, E_3$ are labeled with $+$ on the shape sphere; the three collisions $C_1, C_2, C_3$ are labeled with $\times$. Click and drag on the shape sphere to rotate the view.

The symbolic dynamics of the given orbit (which encode the free homotopy class in the braid group for the orbit) are shown beneath the shape sphere as the non-contractible loops form. Notation is that of Montgomery (1998).

The Start/Stop Animation button, when pressed, starts or stops the animation clock. The Reset Animation button returns the bodies to Simó's initial positions and velocities for the figure-eight orbit.


next up previous
Up: 3-Body Problem Configuration Simulator Previous: The Chenciner-Montgomery Figure-Eight
Matthew Salomone 2003-07-24