On any picture of walking or dancing people one can draw forces.

There is a force mg straight downwards from gravity point of the body. The gravity point of the body is a bit below the heart, let it be heart. Draw a vertical line from heart on to the floor. It is the force vector mg downwards, weight.

Draw a straight line from the contact point of the foot on the floor to the heart. It is resultant force of two rectangular components. One is the supporting force which can be drawn vertically from the contact point of the foot on the floor straight upward to the height of heart. Other is a friction force which can be drawn horizontally from the contact point of the foot on the floor to the end point of vector mg on the floor.

The supporting force upwards is equal to the force mg but to the opposite direction so the vertical forces are balanced.

To be balanced there must be a horizontal force equal but opposite to the friction force. Acceleration produces the balancing horizontal force to the opposite direction of movement on the height of heart during first half of a step while pushing.

During second half of a step deceleration produces the balancing horizontal force to the direction of movement on the height of heart while landing to the end of the step.

I hope Anonymous, Phil, Quickstep or anybody to write the theory of forces more understandably and tell about two instants on every step without fiction or inertia forces. My English is not good enough for it.

sqq. And you are able to think of all of this in .7 of a second if this is the Waltz. I for one am unable. Since the beginning of time these forces have been with us and somehow we have survived without knowing and will continue to do so. In parting and in fairness i believe you are quoting something that is pure science. Dancing is an art and to trying to make it anything other will most times fail.

"sqq. And you are able to think of all of this in .7 of a second if this is the Waltz. I for one am unable. Since the beginning of time these forces have been with us and somehow we have survived without knowing and will continue to do so. In parting and in fairness i believe you are quoting something that is pure science. Dancing is an art and to trying to make it anything other will most times fail."

Yes Anna, we have been doing it this way since our ancestors came down from the trees.

What SQQ has done is to try to explain it. Note the paragraph:

"To be balanced there must be a horizontal force equal but opposite to the friction force. Acceleration produces the balancing horizontal force to the opposite direction of movement on the height of heart during first half of a step while pushing."

What this literally means is that as soon as the body center passes beyond the point of pressure in the standing foot, the body will be FALLING forwards - producing a force accelerating it into the movement.

Nominally we would say that the body is OFF BALANCE, because the forces on the body can only be balanced (neutral) by the inclusion of an acceleration "force"

In contrast, when we say that a body is balanced, what we mean is that the forces on it add up to zero, without including an acceleration.

Now i know where this is coming from. Some of us jumped from a Nut Tree.

As a physicist/engineer, and a dancer, i have to respond to this.
First, Dancing is an art form, as i have discoverd to my joy, as i had never before thought of myself as being in any way artistic.
But just as in music, there are technical or theoretical aspects. There's no harm in thinking about them as this may complement our normal practice and so improve our understanding of dance.
PLEASE...Acceleration is not a force, and so cannot 'balance' a force. If you free-fall under gravity, there is a force acting on you and you're accelerating, but you'd hardly say one balances the other.
Force CAUSES acceleration. And you can't have acceleration (or decelrleration) without a force, otherwise the car industry would be taking advantage.
Back to dancing
The vertical forces from the one or two feet in contact with the floor don't balance the body's weight (mg) unless the body's vertical motion is zero. When we lower, the force from the feet is slightly less, otherwise we couldn't accelerate downward to lower. But when we stop lowering, the force from the feet is greater than mg because we're decellerating vertically. How does this help our dancing? Not a lot i suspect.
The horizontal force from the friction with the floor, does not act at the height of the heart. (BTW i think my centre of body mass is more around my waist) It acts at the floor level. But to stop the body without rotation (as in step 2-3 of a waltz natural turn)you'd need to apply a horizontal force at the centre of body weight, which you can't. So there IS rotation, which the body absorbs through sway and leg and body muscles. Beginners don't need to sway because their horizontal movement isn't great enough.
The body is not a rigid object, so the laws of physics are difficult to apply (some would say thank goodness!). But remember, nothing can defy the laws of physics.
I'd love to discuss this more, if anyone's interested. But it will get complicated!

"PLEASE...Acceleration is not a force, and so cannot 'balance' a force."

Mathematically, acceleration is the result of applying force to a mass.

If you add up the forces f1, f2, f3, etc on a body and the sum is not zero, there is a resulting force, let's call it Fa, which will produce an acceleration a = Fa/m.

Which is also to say that if you add up the applied forces f1 + f2 + f3 - this resulting Fa, you get zero. Fa is our ficticious acceleration "force" - it's not an applied force, instead it's the sum of the applied forces.