Commonly the muscles of the abdominal wall are considered, "core". This is incorrect. Those muscles are surface, the way the skin of an apple is surface to the apple core.
The core muscles are the deepest muscles; they lie closest to the bone (or body center) and exert the greatest control of balance and coordination. Among them, the psoas muscles, the quadratus lumborum, the diaphragm, in the the trunk, and the scalene muscles of the neck and the muscles of swallowing in the throat, as examples -- all of which affect spinal alignment, and thereby, balance. Strength is not their primary contribution, and so the notion of "core strengthening" is inherently misguided.
What is sought through core strengthening is usually stability, but stability doesn't come from strength; it comes from balance.
Balance is a consequence of close coordination between opposing muscles and between muscles and their synergists (helpers).
When a person gets musclebound, as often happens in physical conditioning programs and in cases of injury, close coordination gets distorted, as one muscle or muscle group overpowers another.
Easy balance is impossible when one is in that condition; the person is inherently unstable and muscle tone must shift throughout the body to compensate for those imbalanced in a less-easy stability.
More than that, a person cannot strengthen what they cannot feel, and one can't feel the core if one muscle group overpowers the other. The core can be sensed only when muscles are closely coordinated in a condition of easy, dynamic balance.
Even if core strengthening exercises give equal attention to strengthening all muscles in the (supposed) core group, they don't necessarily give attention to both freeing musclebound muscles and developing balanced (i.e., equal) control/coordination of all of those muscles.
More than that, if muscles of the peripheries of the body, e.g., legs, arms, neck, are musclebound or poorly coordinated, they cause unbalancing pulls from the peripheries of the body to the core. They cause instability that cannot be corrected by core strengthening; they can be corrected only by restoring suppleness and balance among opposing muscles and among muscular synergists (mutual helpers).
So, approaches at core conditioning must have the following two elements present:
- alleviating musclebound conditioning
- developing balanced coordination
Another program that has garnered special interest concerns the psoas muscles, Free Your Psoas, also has that effect. Recognizing that the peripheries affect the core, this program presents a whole-body approach to freeing and integrating the psoas muscles.
Articles on psoas muscle functioning can be found at Somatics on the Web (somatics.com). Other core-workout programs can be found there, as well.