I am going to use an example of what I am talking about from Shinto Muso Ryu jo’s kihon gata, which has to goal to teach you how to use a stick as a weapon. While most of the techniques are pretty straight forward, the techniques forcing the opponent backwards by manipulating the arms after a downward cut, (kuri tsuke [繰付], kuri hanashi [繰放] and tai atari [体当]) are of particular interest because they are perhaps the most difficult to learn and understand. The steps to get into the initial position to perform these techniques is not all that difficult, but it becomes complicated when trying to maneuver the opponent back, which delves into momentum, balance and the use of levers. Combine that with the unwillingness of a training partner to give up position or reciprocate during training and you have a nightmare in the making.
For my purpose, I am going to focus on tai atari (body strike), which is easily found in video form online (see link the link to watch it).
This is coming from seitei jodo, and what I am talking about in this technique, truth be told, is not dynamically illustrated with what they are doing; but it serves as a means to an end.
For the purpose of this topic, the entry to the kata (outward and upward sweep) is skipped over in order to focus on the position where both arms of the attacker are raised and the defenders stick is held vertically across the horizontal sword handle. What comes next is the topic, as a point of departure from that place.
For orientation, the sword is held semi horizontally just above the attackers head, with the blade extending to the attackers right. The stick is held vertically, right hand on top and left hand on bottom, and the majority of the stick’s length is above the right hand meeting the hilt of the sword at some point.
The idea from here is to knock the attacker backward.
The defender pushes back against the sword hilt by focusing the force with the stick above the right hand, while holding the left hand in place. This has a lot in common and is measured in the same way mathematically would calculate the net force used in pushing a car, with a boring dive into mathematic equations involving Newtons, which generally loses an audience. What is happening, in a nutshell, is that momentum from this push forces the attacker’s shoulders back and over the hips, over the center of mass as it rests on a vertical base (along what is called the sagittal plane on humans). After the weight is displaced over the center of mass, the bottom left hand strikes or forces back in conjunction with the stick’s moment inertia (another equation) gathered from the resistance in the attacker’s hilt at the point of contact with the stick.
To sum this up nicely, you use upper part of the stick to push their highest point back and over their center of mass and get them to resist, and then you change the force from the highest point to the lowest point to accentuate it. This is the same principle used to “kick-in” large pillars into place for temples when you need to go deep and it will get wedged and stuck in the hole if it's just dropped in end first with an attempt to hoist it upright.