Core stability is a misunderstood term. Typically, the core is associated with the abdominal muscles groups and stability is associated with isometric or static strength. However in actuality, the core consists of the abdominal muscles groups (transverse abdominis, internal obliques, external obliques and rectus abdominis), hip abductors/ adductors, hip flexors, and lumbar spine.
In addition, it is the lumbar spine that is primarily responsible for posture and stability providing the strength needed for stability especially injuries suffered from auto accidents.