An interesting case of Newtonian mechanics is the three-body problem, which is to model mathematically the movement of 3 bodies. In practice it looks like this:
After centuries of analysis the problem remains essentially unsolved except for a few exceptional cases.
Here is one of the special solutions to the three body problem:
The maths are even more complicated in relativity. According to wiki :
Even the full two-body problem (i.e. for arbitrary ratio of masses) does not have a rigorous analytic solution in general relativity.