Below are some examples of three large bodies interacting under the influence of newtonian gravity. The
equations of motion were derived from the Lagrangian of the system. Both 2D and 3D treatments of the interaction are shown below. The maple script used to generate these images is available for download.
NOTE: The magnitude of the masses were chosen to be of order equal to abs(magnitude of G). Also, There is no physical interaction other than gravity, so the masses can go right through each other.

2D Interaction (No z(t) Dependence)
Two equal masses (red and blue) orbiting each other and traveling to the right (+x direction). A smaller mass (green) approaches their center of mass from the right. Some interesting interaction takes place and the three masses exit to the right. The orbits of the red and blue have become more tightly bound.

Two equal masses (red and blue) orbiting each other and traveling to the right (+x direction). A larger mass (green) approaches their center of mass from the right. Some interaction takes place and the three masses exit to the right. Notice that the red is now orbiting with the green.

Two equal masses (red and blue) orbiting each other and traveling to the right (+x direction). A third, equal sized mass (green), approaches their center of mass from the right. Some interaction takes place and the three masses exit to the right. Notice that the blue is now orbiting with the green.

3D Interaction
Two equal masses (red and blue) orbiting each other and traveling to the right (+x direction). A third, equal sized mass (green), is traveling in z direction. Some interaction takes place and the three masses exit to the right. Notice that the red is now orbiting with the green.

Maple Worksheet for three body interaction. 