One of the biggest problems Ballroom Dancers have is physically staying down in their center. The physical center has a huge influence on the dancer's balance, power and movement. There is a physical center of the individual dancer and a physical center of the partnership. Men appear to have this problem because they are physically connected to their partner at the shoulder level and try to dance through their physical frame. Ladies seem to encounter this problem because they are usually shorter than the man and have a feeling of reaching up.
The dancer's goal is to keep the center as close to the floor as possible. You hear instructors say all of the time: "Stay down in your center". (I always say: "Get down in your saddle".) The student gets down in their center, but eventually they creep back up. The center of the body is typically thought of as being about two inches below the belly button. This seems to be pretty accurate, but the higher level Ballroom Dancers needs to be even closer to the floor.
Let's compare riding a horse to Ballroom Dancing. Even if you have never ridden a horse before, just use your imagination. You grab the saddle horn, put your foot in the stirrup, swing your leg over, sit in the saddle and put your other foot in the stirrup. The goal is to remain in contact with the horse through the saddle at all times. In order to achieve this, the rider has to keep their center of gravity as close to the saddle as possible. It should feel as if your center of gravity is connected to the horses back.
I'm sure you have seen western movies where the "green horn" is riding a horse for the first time. The reins are in his hands, his arms are at shoulder level and he is bouncing all over the place as the horse moves. It is apparent that his center of gravity is way up in his shoulders. If the rider's center sneaks up above the saddle, the rider will start bouncing as the horse moves. The rider must stay down in the saddle to ride effectively.
Does this description of the "green horn" rider, remind you of a Ballroom couple you have seen dancing recently? The "green horn's" arms are at shoulder level. The Ballroom dancer's frame is at shoulder level. The rider is bouncing and almost out of control. The Ballroom partnership is moving awkwardly and fighting to stay under control. It is quite common for new and inexperienced Ballroom dancers to try to dance with their center of gravity in their frame because that is where the partnership is physically connected.
The ultimate goal is for the Ballroom Dancer to be in their "center" all of the time. The "center" is the part of the dancer's body that is touching the seat of the saddle. I'm sure you have heard the expression: "Flying by the seat of your pants". This refers to the pilot feeling the action of the aircraft through his/her "center". The same is true for the Ballroom Dancer except the dancer is feeling the partnership of two people and the pilot is feeling the partnership between him/her and the aircraft.The ability to dance through the "center" is not the problem. It is relatively easy to dance through the "center" once the dancer has identified the "center" and knows what it feels like. Maintaining the "center" throughout the dancing is the problem. The rise and fall in Waltz is a good example of the use of the "center". The rise and fall happens through the ankles and knees. This makes the dancer's body go up and down. Remember that the Waltz body starts from the hip sockets and goes up. The ankles and knees are pushing up against the top of the saddle thus making the body (sitting on the saddle) go up and consequently down. The body is not involved in the up and down movement. (At very high levels of dancing the body stretches as well.) All movement (in all directions) happens through the "center". Rhythm/Latin, Smooth/Standard, it is all the same as far as physical movement is concerned. The beginning Waltz dancer (and often the advanced social dancer) will frequently lose the "center" and start rising and falling through the frame. If the leader loses the "center" it is likely the lady will too because she is dancing through feeling.
It is hard to "turn on" the "center" only while you are dancing and expect it to stay there for the whole dance. The "center" needs to become part of who you are. If you encounter professional Ballroom Dancers off of the dance floor (and I have), you will notice that they appear different than the average person. Their posture is perfect and their movements are precise and centered. They carry themselves differently, and move differently because of their Ballroom dance training. These dancers have good posture and are centered all of the time, not just when they are dancing.
It is relatively easy to be in your "center" while you are thinking about it, but once other things start happening (movement, music, partnership, etc.), it is easy to slip out of the "center". The most effective way to "stay down in the saddle" (be centered) is to be there all of the time. Make it part of your everyday life. "Live in the saddle".