Relative Body Balance
Relative Body Balance is the most important scientific concept to understand and utilize in martial techniques. Most internal martial arts will talk about this vaguely. They will stress its importance, but I have never really seen an explanation of what it is.
Relative Body Balance is simply the acknowledgement and use of Newton's third law of dynamics to move efficiently.
Whenever a body exerts a force on another body, the latter
exerts a force of equal magnitude and opposite direction on
the former.
Because of this principle every part of the body is affected when any other part moves. "Good" relative balance is achieved when this governing principle of motion is effectively used to maintain upright balance, achieve locomotion (displacing the center of mass), and to move a limb with great force, speed and/or accuracy.
Just as machines need to be properly (counter) balanced in order to perform smoothly and effectively, so do biological bodies. This counter balancing is easily visible in the way that we swing our arms when we walk, when we run, when we spin sideways... If we ignore, or worse, fight this natural counter balancing in our martial techniques our performance will be suboptimal.
Improving Relative Body Balance
Relative body balance can be studied abstractly but it can only be improved through practice. The word balance is not just a metaphor for this principal, but it is our sense (of balance) that we are talking about. We develop it when we first learn to walk, and as other forms of balance such as riding a bike, skiing or surfing we can only learn it through experience. Even though describing what 'good' relative body balance is like, will not allow you to 'get it', it will help guide any exercises you undertake to improve it.
Random bids below here, major brain dumping occuring, may not make sense yet
Dynamic Balance
RBB is a mainly a dynamic thing. It is hard to describe static balance just as it is hard to explain to someone how to balance themselves on a bycycle standing still without pedaling and rolling.
Counter balancing vertical movement is more important for efficiency, less for balance. It is easier to lift a limb if another linb is lowering keeping the COM in place. This is similar to the couterweight on a elevator. counterbalancing adds more mass to accelerate, but aleviates fighting gravity since their is no potential change.
Things get easier the more you do them, not nec. because of muscle strength, but because of better RBB. Unlike muscle strength, RBB stays with you. Just like riding a bike, once its learned, you never forget it. Of course, it can always use refinement and refreshing.
Efficient Rotation:
To rotate efficiently, a human must take advantage of inertia.
Inertial rotation requires that the rotating object rotate around an axis which passes throught the COM of the object.
What this means is that if you attempt to rotate an object, say a hammer, you can physically rotate it around any axis, but if you are not rotating it around its COM than you will be contantly providing external input (force or energy) to the hammer. If you throw the hammer you will no longer be able to provide external input to the hammer and it will rotate inertially (in a vacuum). No matter how you tried to rotate it before releasing the hammer, once you release it, it will only rotate about its COM!
How does this apply to humans?
To rotate our full body inertially, we must rotate around an axis passing through our COM. In order to stay upright, this axis must specifically be the vertical axis. With practice one should be able to efficiently rotate around once's central axis quite easily and efficiently.
It is important to be aware of the changing location of this axis depending on the changing shape of our body, because if we change the shape of our bodies in a way that causes any horizontal translation of our COM, then this vertical axis will also have to translate, even if our feet have not translated!
If we are rotating with our feet together and our hands at our sides, we will quickly find our central axis and rotate around it. But if we lift our arms and hold them out directly in front of us we will shift our COM forward. If we do this standing straight without rotating we might notice the COM shift but it will be subtle since it will probably just shift towards our toes a bit (as long as we don't adjust our hip posture to couterbalance our arms). But as soon as we try to rotate the change should be much more perceptible because we can no longer rotate efficiently around the same axis since it no longer goes through our COM!
If we now take this example to the extreme and shift our COM (actually a mutual COM) well outside of our feet by holding hands with someone else and spinning facing each other (the way children often do), we can see that it is much more difficult to spin around our personal COM axis which resides above our feet than around the joint COM which resided somewhere between both people.
If we practice efficient rotation, again with our feet together, we will find eventually that we adjust our posture slighty differently from a normal standing posture. With this adjustment one should eventually settle into a position that creates a strong crisp central vertical axis we can easily feel. This adjutsment is the lifting of the hips and you will find this adjustment described in many different athletic endeavours, gymnastics, dancing, running, skiing... Watch a gymnast on a balance beam. Once they have mounted the beam and prepare to walk along it, you will notice them adjust their posture, typically lifting their hips (causing their back to straighten).
The Center of Mass
This doesn't real fit here, how do we integrate this before we talk about COM above?
The human center of mass (or gravity) is often called the "center" in martial arts circles, other common names are "hara" and "tantien", although these terms may not always refer to the actual center of mass so we will not use them. In a normal standing position the center of mass is usually located about 2 fingers below the belly button and three fingers in from it. But since we are not rigid objects, the human center of mass can change positions. The easiest way to think of this is is by imagining oneself bending over and touching ones toes. By doing this we have almost halved our height, our center of mass certainly would not stay where it was near our belly button, but rather, it now must be lower.