When my husband and I visited Hawaii, we encountered a couple of exercise groups on Waikiki Beach. One was a Pilates class. The instructor had the class members do the V-Sit. They looked like it was an effortless exercise, but in reality, it's not! This exercise involves holding the entire core firmly, breathing fully, while balancing on your tailbone.
For Beginners and those who are trying to improve: First, sit with your knees bent, heels touching the floor. Compress your core by taking a deep breath, then squeeze some of the air out by pulling all of the muscles in your abdomen, sides, ribs, and back firmly in like you are wringing the air out. With your core held firmly, breathe fully by filling up your lungs from top to bottom, then exhaling fully. Place hands behind your thighs like the picture of "Jars of Clay" from PraiseMoves, then lift the heels off the floor. At first, you might round your back, but resist the urge. You can always go back to the beginning to reset your posture.
For intermediate level: Grasp your heels and straighten one leg at a time. If you keep your back from rounding and your core compressed, you will be able to sit only on your tailbone. If you are having trouble holding, try stretching your hamstrings first, then try again. For advanced "Jars of Clay", let go of thighs, lean back straighten legs out with only your tailbone touching the floor, arms go out to sides with hands palms up.
Keys to this exercise: firm core, head in neutral alignment (ears lined up with shoulders), and concentration on each area of the body.
Main core muscles worked: Diaphragm, intercostals, internal and external obliques, rectus abdominus, iliopsoas group.