The Physics of Toppling and Regaining Balance during a Pirouette

Abstract

One of the most common movements in dance is a turn around a vertical axis with one supporting foot on the floor—a pirouette. If the pirouette is not performed with the body on balance, it is not consid-ered successful. Dancers are often taught to perform successful pirouettes by beginning the movement on balance and then keeping the body in that configuration, as opposed to correcting for an imbalance with small adjustments during the turn. Many, even advanced, dancers have significant difficulty performing more than two or three turns in a pirouette before losing balance, despite continued trial and error efforts to improve. To describe the mechanics of toppling and control of toppling during a pirouette, a theoretical model of a dancer in standard pirouette position was created, and an experimental study of real dancers performing pirouettes was conducted. Body segment parameters for the model (mass, length, etc.) were based on anatomical data and adjusted for sex, total body mass, and height. The principal moments of inertia were determined for several hypothetical dancers, and rigid body equations of motion numerically solved to express topple angle vs. time. When dancers reach too large a topple angle, they are forced to compensate by either hopping on the supporting foot in an attempt to regain