Hi Rosetta and Gary -
For exercises targeting the core and also flexibility, have you checked the Chi Living channel - http://www.youtube.com/chilivinginc?
With Chi Running and Chi Walking, the first thing we address is alignment - where your shoulders are over your hips and your hips are over your ankles. By setting this up first (in the posture lesson) you feel what that alignment feels like as you are standing in place. From there, as you lean slightly forward from your ankles, you’ll notice some tension in your low abs. It’s that tension you want to hold to maintain a stable pelvis - keeps you from bending at the waist and keeps your hips from rocking side to side. Most people lose that when they go into running, so paying attention to that engagement (just enough to maintain stability) helps tons.
Paying attention to that throughout the day helps you integrate that into your body quicker so it’s there when you start to run. You can still do core exercises to help strengthen the surrounding areas (especially if you have some really weak areas, such as the glute medius, at the hips), but with Chi Running, you aren’t relying on overall glute strength to move forward as much as you are relying on the lean and pull of gravity to move you forward.
This all takes time to integrate into your body, especially if you have old habits to overcome, and it takes patience. The core gets stronger as you progress, and the aerobic capacity increases, too.
Hope that answers your questions!