The fine art of body dropping or "tai otoshi" is the ability to suddenly drop your body but keep your alignment intact as you do so. It is a crucial part of TSYR and I enjoy training this body movement. It is not as easy as it sounds. What tended to happen when I first tried this was that I would let my arms "float". Or, as I dropped my body, my hips would pop backwards and ruin my alignment. Both these things are detrimental to keeping connection to your partner and maintaining good body alignment. The idea is to drop through your spine, this requires a completely upright posture through the whole movement.
Please don't confuse what I am talking about with the tai otoshi used in judo like throws. It is not a technique in itself but a body principle. Once I had some idea how to do it, I could use the body drop to throw partners once kuzushi was made. The effect is fast and dramatic and often it occurs before your partner realises what is happening. There is no 'tell'. As body movements such as these are refined, it gets harder and harder to tell when the uke/uchitachi is about to be thrown. It comes down to complete control of your own body to control another. The more you can isolate and manipulate your own structure, the easier I is to manipulate someone else on contact.
Of course the conditioning exercises that we do to develop a budo body aid in also developing such movements as tai otoshi.