There are 8 Principles of Pilates:
The core comprises of several muscles: the transverses abdominis, the pelvic floor, the diaphragm and multifidus. These deep muscles create a cylinder of muscle in the lower abdomen. Each has an important anatomical role to play as well as an important role whilst doing pilates exercises.
The transverses abdominis (T.A.) holds in the stomach contents. The pelvic floor is a sling of muscle creating the base of the cylinder. The diaphragm plays an important role in breathing. During normal breathing the diaphragm contracts whilst breathing in and relaxes whilst breathing out. Multifidus is a muscle found in back, it has a role in stabilisation.
When the core engages, multifidus, the T.A. and the pelvic floor co-contract. After trauma, especially back trauma the core may cease to activate spontaneously but can be trained to re-activate. During Pilates the healthy core is consciously engaged so that it may be strengthened as it responds to Pilates moves.