Simulations

Using the GW Orion System we prove an example of a stable Two-Body Orbital System

We now introduce a third body but set its mass = 0, this restricted scenario is referred to as the Sitnikov 3-body problem.
We can see that the original two-body system maintains an oscillatory motion.

The Sitnikov Model with a third mass of minute magnitude continues to show an oscillatory motion
of the original two-body system. 

On the next step we equate all three masses such that m(a) = m(b) = m(c).
This results in a singularity where all 3 masses come together. This is a restricted and predictable 3-body problem.

We now introduce the complete 3-body-problem, where 3 bodies of different masses with different initial velocities
are introduced close enough for their gravitational forces to interact. We see two bodies within the system remain stable momentarily, until the third body disturbs their predictable motion.
The system only re-establishes stability with one of the bodies exiting the system.