Possibly the most important part of core stability is also the most under looked. Your ability to rotate your upper body and lower body independently is crucial to injury prevention and athleticism.
It is one thing to have strong abdominals and a strong lower back but if you rotate and especially rotate and lift you can still end up in trouble.
The thing is it is not just your obliques (sides of abdominal area) which provide stable strength but also your psoa’s muscles. (See pic below). To develop rotational stability and strength requires working both together.

To better picture this see in the video how the lower body is anchored as the upper body rotates. The lower body is actually working through the inner thigh to counter rotate as the prime movers (your obliques) turn in the opposing direction
This is the foundation of core stability. Stay tuned for part 2!
Be well, be strong,
Andrew and Tierney