Consider the simple problem of a block sliding on a rough surface, being pulled by a linear spring. The resulting motion is unpredictable and non-deterministic. In general rigid body dynamics problems involve friction and here is were determinism breaks down.
Ignoring friction things might seems look better, but then we enter the area of joint singularities (gymbal lock and knee locking) causing non-determinism in time evolution. The actual solution relies outside the realm of rigid bodies, as body deflections and joint compliance must be considered.
For example with thin slender structures, you may have buckling which is unstable and not always predictable which way it is going to deflect. Try compressing a ruler on its ends and see what happens.
So the question is, under what conditions/assumptions do you want to bound determinism, because general determinism does not exist.