Gyrotronics is developed by Julio Horvath and basically combines a bunch of popular workouts such as yoga, ballet, tai chi, gymnastics, and even resistance training.
The main effective ingredient of Gyrotronics is the Gyrotonic Expansion System, or GXS. The exercise is very new, so visit the Gyrotonic website if you are interested in learning more. Oh, and the exercise has nothing to do with eating a Gyro unfortunately. - Source: By Feedback Daily blog.
In it's official website Gyrotronics is detailed in principles. "GYROKINESIS® principles that form the foundation for this novel approach to maintaining health and well-being after many years of study, as he not only tried and succeeded in repairing the bodily injuries that he sustained as a professional dancer using these new methodologies, but he also sought to create a system of exercises that anyone could perform, regardless of age or state of health."
Read more about Gyrotronics at at eMaxHealth Exercise and Fitness Column.