Had to grab my book for this. Phillippe Karl, past head of Cadre Noir in "Twisted Truths of Modern Dressage" - on engagement of the hindquarters and propulsive force - This theory of the shortening of the horse's frame by jointly developing the 'propulsive force of the hindquarters and their 'engagement under the horse's body' is very appealing to the mind, but it does not withstand analysis. ...It is naturally through forwards movement that the rider develops the 'propulsive force' of his horse. However, it is the extension of the hind leg which propels the mass, or in other words its disengagement. Propulsive forces do lower the haunches, but this is by extending the lumbar back and pulling the hind legs out beyond their natural plumb line (frame which lengthens), the opposite of the official theory. ... In terms of locomotion, "development of the proplusive force: and engagement of the hid legs under the body" are absolutely incompatible. This concept of the horse which shortens its base due to the engagement of the hindquarters resulting from the development of their propulsive force is one of the dogmas of modern dressage. The laws of locomotion disprove it categorically.
The official drawing in the FN Guidelines for Riding and Driving German Equestrian Fed. Showing a horse which flexes it's haunches and shortens its propulsive base energetically in trot towards the rider's hand, illustrates the obsession of a system, but in no way resembles reality.
While I didn't type a few sentences of deeper explanation, Please, Please read this book! Taken from pages 76-77. This is a fantastic read.