I wanted to share with everyone what "The Bone Man" as he calls himself is sharing. Thank you! and also I would like to thank Tova for asking him
You can find David's website here. David is the man behind Yoga Anatomy Vol 1 and 2, "Introduction to Anatomy for Yoga Practitioners". (picture right from here).
I'm hoping that I can bring a little bit of simplicity to this conversation. Tova asked me to weigh in.
There are two movements that are getting mixed together here. First, there is pelvic rotation which is described as an anterior tilt and a posterior tilt. These are defined and discussed from neutral or what is referred to as anatomical position (someone standing upright basically)
An anterior tilt is when the pubic bone moves downward and whenever this happens we naturally make more of a lumbar curve, like a backbend. A posterior tilt is where the pubic bone rises or lifts and the opposite effect naturally happens in the lower back, we reduce the lumbar curve. These movements happen as the pelvis moves around or at the head of the femur.
Nutation and counter nutation are movements that happens at the sacroiliac joint, that is where the sacrum meets the two sides of the pelvis. Nutation (from neutral again) is where the top part of the sacrum would move down and forward relative to the pelvis being fixed in place. Kapandji referenced above describes this as the sacral base moving forward and down. Counter nutation is simply the opposite.
Everyone, unless their sacroiliac joint is fused, does some nutation and counter nutation. The average person probably has somewhere between 3 and 5 millimeters of movement at their sacroiliac joint. In other words, not a whole lot. I'm surprised sometimes by how much emphasis there is on this movement in backbending type poses with such a small range of motion there.
It is always a good idea to consider all of the factors that go into a backbend and not get caught up in the part that moves the least. A good or deep backbend has much more to do with the hip flexors, such as quadricep, adductors, and the iliopsoas being open enough to allow the pelvis to not get jammed up in an anterior tilt and compressing the lumbar region.
Since the question is regarding nutation and counter nutation... when one is in a deep backbend, your pelvis (relative to neutral) is in an anterior tilt. These forces will naturally put a force on the sacroiliac joint and if we look at the movement created there it would be counter nutation. It also possible that the sacrum maintains its relationship with the pelvis and is not doing either, but the forces on it if we took away all of the ligaments somehow, would be counter nutation.
This in no way speaks to what ones intention might be while in the pose though. you might naturally try to undo some of the pelvic tilt, as people do when trying to tuck the tail bone under. this would be trying to tilt the pelvis more into a posterior tilt from an already extremely anteriorly tilted position. So it's not like it's going to put the pelvis into a posteriorly tilted position because you're not starting from neutral. If you do this, it would undo some of the counter nutation and potentially allow the sacrum to nutate slightly.
People who are naturally flexible will naturally have more movement at their sacroiliac joint. They may actually feel this, or control this movement better than the average. I certainly can't argue with anyone's experience.
I also wouldn't suggest trying to get a student to do this movement specifically, it kind of will... either happen or not happen on it's own. However, if someone is dealing with sacroiliac dysfunction or pain, it would then be appropriate to pay more attention to how much or little of this movement is happening.
David Keil"The Bone Man"
Female pelvis picture comes from here