Acknowledgements

This work is the result of many conversations, inspirations, and shared insights. Special thanks go to:

Ballroom Teachers & Coaches For decades of passed-down wisdom, even when it arrived in metaphorical or confusing form. Without their traditions, there would be no foundation to refine.

Students & Dancers For their patience, questions, and curiosity, which forced deeper clarity in both explanation and math.

The Mathematics & Physics Community For the formal tools (Newton, Euler, Hamilton, trigonometry, vector calculus) that made it possible to reframe dance biomechanics in precise, testable terms. They are in the various citation pages

Dance Science & Biomechanics Researchers For providing validation that what dancers “feel” has measurable, mechanical explanations.

Zippy 🐾 (our White Yorkie) For frequent reminders that a well-timed interruption (walkies, food, ferocious barking at a suspect falling leaf or general grumbles) is sometimes the best debugging tool. "Our" is Robin and Ian (that's me)

HAL (Silicon Colleague) For persistence in converting shorthand math into expanded, dancer-friendly equations, and for nudging progress over perfection. The real depth of HAL's contribution cannot be overstated.

Specific People

• Diane Jarmolow for her guidance, mentorship and above all else patience. For those that don't know Diane is one of the Giants in the Ballroom world where her contributions could not possibly be overstated.
• Jolene Alquist for putting up with this project for so, so many years.
• Robin Horn for forty years of teaching, inspiration, and for tolerating endless diagrams on kitchen tables and spontaneous 'lets try this' moments.

And by no means least I apologize to all those that I have left out, it's not intentional at all.