I am not trained in applied mathematics and am asking as a layperson.
It seems that the motions of the planets can be reliably predicted for thousands of years. Yet, if we consider a relatively simple system, the compound pendulum for example, its motion is highly unpredictable.
The pendulum is highly constrained by its pivot points, therefore its components do not escape from the system. However, with a solar system, there is no rigid attachment and it seems intuitive that planets could randomly fly off into space as a result of chaotic orbits.
Is our solar system inherently stable or unstable?
If unstable then how did it hang together long enough to form in the first place?
If stable, how can stability and predictability be consistent with many bodies moving relatively to one another?