First of all, let's define contraction. There are three main types of skeletal muscle contractions: concentric, eccentric and isometric.
In a concentric contraction, the force generated is sufficient to overcome the resistance, and the muscle shortens as it contracts. A good example of a shortening muscle is a traditional biceps curl with a dumbbell. The bicep becomes a short bump. Actually, the word muscle is derived from this action; musculo in Latin means little mouse. It seems that the movement of a contracting muscle under the skin is reminiscent of a mouse moving beneath a rug.
In an eccentric contraction, the force generated is insufficient to overcome the resistance placed on the muscle and the muscle fibers lengthen to lower a load, as in the downward movement of a bicep curl. In Pilates, an eccentric contraction is often used as a means of decelerating a body part or an object, such as returning the reformer carriage home via a deceleration of the hamstrings. Part of the genius of Joe Pilates was in the eccentric training via deceleration of the springs on the Reformer, Trap Table and the Chair.
An isometric contraction occurs when the muscle remains the same length despite building tension. An example of this from our repertory is when we add tone in a static pose such as a quad stretch on seated on the roller with one shin tucked under. The tone you feel when you 'scissor' the legs is an isometric contraction.
So, which muscles are firing in the co-contraction?
The co-contraction IS your core musculature: they are the muscles that support your spine, especially in the lumbar region. They roughly form a cone shape with the apex at the solar plexus and the wide base at the pelvic floor.
The muscles involved are the internal obliques, the transverse abdominus (TA, for short), the posterior fibers of the psoas, the multifidus, the anterior portion of the pelvic floor and the breathing diaphragm. When they work in concert, they co-contract to become a strong corset of internal protection.
This is what Joe Pilates referred to as the Powerhouse.