All Martial Arts should be thought of as physics that is applied to the opponents body for defense or offense.
There are variations to take-downs, throws and sweeps, However, the nucleus of each variation is process of moving the center of mass away from the supports [usually the opponents legs], or moving the supports away from the center of mass, and then continuing to move so that your opponent cannot use movement to bring their center of mass back above their [supports] and weight. Although it seems as a simple concept, it is highly important during rolling in regards to posture. Posture being head aligned with your hips. If your head is misaligned, you are either going backward or forward as the opponent moves the center of mass away from your supporting hips.
[Physics is the branch of science concerned with the nature and properties of matter and energy. The subject matter of physics, distinguished from that of chemistry and biology, includes mechanics, heat, light and other radiation, sound, electricity, magnetism, and the structure of atoms. For (all) Martial Arts, (the premise would be the mechanical part of physics.)]
Newton's Three Laws of Motion
1st law: (Law of Inertia)
An object not moving will continues to not move, or if moving, will continue to move in a straight line and at the same speed, unless it is made to change its speed or direction by a force. If there is no force, the object will keep on doing what it is doing. We do not see this often on the earth, since there are a lot of hidden forces action on objects all the time, such as forces from rough surfaces (friction), air resistance, etc. In rolling, we apply the concept of inertia, by getting out of the way of a charging person, since his/her own inertia will make it hard for them to stop. If you do not get out of the way, their inertia will make it hard for your to stop them. You will have to apply a large force to overcome their inertia or to redirect them. With people, the concept is different when it comes to tricking the force to go in a different direction, thus the eyes play an important role when coercing force to stop and switch to a different direction.
2nd law (Force = mass x acceleration)
If there is a force on an object, the object will either change its direction of motion, or change its speed, or both. The acceleration of a body is directly proportional to the net force acting on the body and inversely proportional to the mass of the body. That is, the more force you apply to an object, the greater the rate of acceleration; but the more mass the object has, the lower the rate of its acceleration. Forces can be applied to the body to cause compressional tissue damage (i.e., joint locks).
3rd law: (Law of Action and Reaction)
To every action force there is an equal and opposite reaction force. When you push on an object, the object will, in turn, push on you. Note that there must be two objects; the one pushing, and the one being pushed. You can not propel yourself forward by patting yourself on the back. If you are going to push on an opponent, you need to be braced against something like the ground, or you will be thrown off balance as well as your opponent. If you have ever practiced standup throws think about the most basic uchi mata (https://www.youtube.com/watch?v=XBYFsesDNm4) the push creates a reaction (from your opponent) whereas the throw is the action.
Thus there is a science to Jiu-Jitsu and this includes the aforementioned mechanical aspects of physics including what I have coined as the "Three Keys of Jiu-Jitsu"... Grips, Hips and Counterbalance. Applying grips is essential for control and feeling direction. Your hips play the most important role as fluid hip movement is necessary to combat your opponents force. Hips also plays an important role in locking down the position AND executing the submission. If you do not apply your hips while executing any submission, chances are you will not get taps when going up against higher level players. Many have asked me "What is counter-balance?" and I reply to them it is feeling the force of the opponent as it relates to your position. Then they angle their head and frown... Most do not understand - so the best way to explain it is as follows... Depending on the position you are in (top or bottom) do you feel their force going forward or back? Do not fight force with force, either move with the force (hitchhike) or take the force into a redirection. Do you feel your opponent posting to the left or to the right? if they are posting to the right, go to the left and vice-versa... manipulating your opponents base (center of mass) works best with proper grips applied and fluid hip movement. Three points just like the triangle in Jiu-Jitsu... Oss