A key to improving balance is learning how to stabilize the body.
Often times stability comes naturally; we naturally stand with our feet wide so that we don't have to worry so much about balance. Or we bring our center of gravity closer to the earth so that staying balanced isn't so difficult.
As an example of the former case, balancing with feet together is a bit more difficult than with feet apart because the area of the foundation is smaller.
With a smaller foundation we have to work harder to keep our center of gravity over our foundation. Height further increases the difficulty.
As an example of this, bakasana is more difficult than standing upright because our hands offer a smaller foundation than our feet. But handstand is more difficult than bakasana (or crow pose) because the center is so much higher up in this inverted yoga pose.
Bakasana is also relatively easy because the legs are resting on the arms. This connection between the arms and the legs makes balancing easier because the arms support the knees which then support the pelvis. We then don't have to worry so much about the pelvis wobbling around. The connection between the arms and the legs helps to make this pose more stable and thus easier to balance in.
In handstand, not only is the center of gravity very far away from the ground, the shoulders are also between the center and the ground. This means that the shoulders (and arms) have to be very stable in order to make balancing easier. If they aren't stable then the shoulders will move forwards or backwards, carrying the ribcage, pelvis and legs with them, and that will make staying balanced very difficult.
What can make it easier is learning to control the shoulders so that we can use them to keep the ribcage where we want it to be. While the legs waving around can still make handstand difficult, I'd suggest that the shoulders are one of the first places to start to get better stability and control in handstand. It's like standing upright and balancing, if your feet and hips are stable the job is that much easier.
How do you learn to take your feet off of the wall in handstand?
Balancing in Handstand tells you how.
An interesting pose to practice stabilization is the arm balance called Galavasana. It's also known as flying pigeon because of it's similarity to pigeon pose. And actually pigeon pose is a good way to learn some of the necessary stabilizing actions in this pose.
When working with beginners or people new to pigeon pose one of the actions I often teach is how to lift and lower the hip of the front leg.
Initially you can do it using the arms to support the weight of the upper body (shown above).
But the idea is to learn to use the leg itself to help lift the hip and lower it (shown below).
Pressing down with the knee activates the muscles along the outer thigh and outer hip. That downwards force at the knee results in the hip on the same side lifting.
Then while holding pigeon pose, the job can be that of maintaining enough pressure to keep the pelvis level from left to right while at the same time reaching the back leg further back so that the pelvis gradually sinks (second picture below).
The reason I use this as an introduction to galavasana arm balance is that a similiar action is used to lift the hips in galavasana. For this arm balance the shin rests against the back of both arms. It can be very uncomfortable so you have to find a way of positioning the shin so that the muscles at the back of either arm (particularly the one closest to the knee) are comfortably out of the way.
With weight on the standing leg and the hands on the floor, the idea is to lean forwards and actively press the shin into the backs of both arms so that the tension in the leg causes the pelvis to lift. If your weight is far enough forwards you should then be able to relax the supporting leg and lift it.
This is an example of using tension to create stability. Then tension in the front leg makes it easier to lift the pelvis. In this case the tension doesn't lead directly to improving balance. Instead it provides lift. We'll look at headstand next to see how stability can directly help in improving balance.
In bound headstand, particularly bound headstand, which is a fairly common inverted yoga pose, the elbows and head ideally form a triangle shape.
If the elbows are too wide then we lose the triangle shape and the foundation becomes more of straight line, offering as much stability as standing on a single skate.
If the elbows are about shoulder width apart then the triangle forms a base that potentially gives the pose stability both in the front to back direction (longitudinal) as well as the left/right direction (transverse.)
I say potentially because just configuring the head and arms in a triangle shape isn't enough to balance in this pose. To stay balanced in this pose the elbows have to press down into the floor.
What creates the pushing force that drives the elbows into the floor? The shoulders.
To improve balance in headstand (or to be able to get up into headstand in the first place) one of the exercises that I have my students practice is moving the shoulder blades outwards and inwards while standing upright with hands clasped behind their head.
In this exercise, moving the shoulder blades outwards (protraction) will cause the elbows to lift while moving the shoulder blades inwards (retraction) will cause the elbows to lower.
Upside down in bound headstand, to increase the downward pressure of the elbows, spread the shoulder blades. The muscle that causes protraction is the serratus anterior muscle. And in bound headstand this muscle works against the weight of the body to help stabilize it.
Pressing the elbows downwards with just enough pressure, we can keep our center of gravity over our balance point.
If our weight shifts forwards then we can increase elbow pressure to push our body backwards.
If we feel our center going the other way, and if we respond early enough, then letting the shoulder blades move towards each other, we may be able to reduce elbow pressure enough that our weight shift forwards to where we want it to be.
Note that neck tension is also important in headstand in order to keep the neck safe.
Rather than working against the weight of the body, the muscles of the neck work against each other to keep the neck stable.
Now with the hands clasped behind the head in such a way that the sides of the palms are also on the floor, if you find your weight shifting back then you may be able to use hand pressure to push your center of gravity forwards. In this case it is the triceps muscle (at the back of the upper arm) that is used to increase tension.
In either case, the more you use your connection with the earth, the easier it is to improve balance.
How do you safely prepare for headstand? Bound Headstand includes step-by-step sequence of exercises to get you ready for this inverted yoga pose.
One of the easiest ways to improve balance is to practice weight shifting while standing.
While standing upright, I'll often have students shift their weight back and forwards. In the weight-forwards position I'll have them notice their toes. In general while shifting forwards, as the center of gravity moves over the toes and forefoot, the toes automatically press down.
What happens if you try relaxing the toes (while keeping your center in the same position). If your weight is forwards far enough you'll fall forwards. The tension in the toes is what enables us to stay balanced if our weight is forwards.
If you shift forwards slowly and smoothly enough you may notice a gradual increase in toe pressure.
You may also notice a gradual decrease in heel pressure. These pressure changes tell us that we are shifting our weight forwards.
Balancing on the fronts of our feet the ideal can be equal pressure at toes and forefoot. If we feel our toes press down with greater pressure then this is an indication that our center has shifted forwards. Why, because the muscles at the bottom of our feet have to exert more tension to keep us upright. This increase in tension is a signal that our center has shifted.
The response is to boost the tension even more so that instead of just keeping our center where it is we actually push it back.
By the same token if our center shifts back then the toe tension will decrease. The muscles of the feet don't have to work so hard because our center has shifted rearwards. If the shift isn't too far then relaxing the toes further may be enough to cause our center to move forwards.
If our center has already moved somewhere behind the front of the foot then we are too late, we'll have to use some other means to get our center back over the fronts of the feet.
And this is why being sensitive, being aware is so helpful for improving balance. If you learn to feel your center shifting early enough, you can act with minimum effort.
Balancing in headstand we can use the same principle. If our weight shifts forwards we'll feel it as an increase in downward pressure at the elbows. The response can be to press the elbows down with even greater pressure to shift our weight back. If our weight shifts backwards we'll notice it as a decrease in elbow pressure and/or an increase in pressure at the crown of our head.
Note that in both cases it is tension or its lack that helps us to feel our body. But it is also tension that can help us stabilize our body so that it is less likely to go off balance in the first place.
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A key element nearly any yoga balance pose is learning how to stabilize the body. I've included some examples in Improving Balance.