Many people think that all you need to balance on your arms in yoga is strong arms. While there is no substitute for a solid foundation in your shoulders and upper body if you do all the work of arm balances and inversions with your upper body you miss the inner work of yoga. A careful development of core strength will help take your arm balances to the next level.
It took me a long time before I was convinced that a little activation of my pelvis would make a difference in arm balances. But the logic is pretty simple and overwhelming when it comes to building up a strong core. Your arms are relatively small in comparison with the total weight and mass of your body. If you ask your arms to do all the work while your body does nothing it’s an unfair and unrealistic burden to place on such a small part of your body. If you rely on only your arms you will need massive bulk through the upper body to hold your body off the ground. If you think instead that each part of the body is responsible for lifting and being strong itself then you will have not just the strength of your arms but the strength of every muscle in your whole body to lift up. If you engage your pelvic floor you will gain direct connection into your center of gravity. If you control your center of gravity you control how your body moves through space. When the whole body is engaged and united around a singular activity there is also a synergy between the whole network of muscles ad energy that creates more strength than any one muscle on its own. Distributing the work of the posture throughout the whole body is more balanced and does not overuse or stress any one muscle or joint. Building a strong core is an efficient movement pattern that prevents lower back injury and keeps the body in healthy alignment.
Try a simple movement like this to tune into the combination of core muscles and abdominal work that will improve your arm balances from within. Lying on your back engage your pelvic floor, bend your knees and stretch your arms out. Then lift your hips up and forward to place yourself into a modified crow posture while reclined. Visualize your pelvis and torso strengthening to hold your body in the posture. Next time you are in crow posture, Bakasana, consciously activate the same muscles and use the activation of your core strength to lift up even higher with less effort.