I never liked calling it "core" training. It's so much more. Regardless, it is Ab, lower back intensive as we are going to stabilize many movements with the incorporation of those muscle groups through single arm or leg movements be it contra-lateral or ipsa-lateral.
All the motions today are done with feet up and no other movements to compensate for either the weight being used or the speed by which it is being moved. If there is, simply reduce the weight and contract the abs harder to limit or nullify the leans and jolts.
Today's Training:
Push Ups: 3x10
AirDyne (arms only) 10 minutes
Single Arm DB Flat Press: Work up to a weight that the motion is only shoulder extension, and elbow extension. Feet should be up and watched for any compensation. Once the weight is found, three working sets of 8 reps on each hand.
Single Arm DB Incline Press: 3x8 Same set up
Single Arm DB Supine Tricep Extension: 3x12
Cable Rope Tricep Push Down: 3x12
Bike Commute: 21 minutes.