Using Biomechanical Optimization to Interpret Dancers’ Pose Selection for a Partnered Spin

Many people all over the world enjoy swing dancing. Dancers often talk about using the laws of physics in performing their physically rigorous jumps, lifts, and spins. However, they do not have mathematical evidence to support these claims. Our goal was to determine whether expert swing dancers physically optimize their pose for a partnered spin. In a partnered spin, two dancers connect hands and spin around a single vertical axis. We describe the pose of a couple by the angles of their joints in a two-dimensional plane. Optimal values for these angles were outputs of an optimization model that gave the ideal pose for a couple. A biomechanical model built in Mathematica allowed comparisons to live dancers with the use of a motion capture system. The optimization objective is to maximize estimated angular acceleration. The model considers only external forces and neglects internal forces. It consists of equations derived from physical principles such as Newton’s laws and moment of inertia calculations that govern how people move. Using numerical non-linear optimization we found the pose for each couple that maximizes their angular acceleration. Different dancers are differently sized, so every couple has a different optimal pose. Each couple’s optimal pose was compared to the pose they actually assumed for the spin. Our motion capture system recorded the three-dimensional location of each of the marked body joints. We used this data to determine the angles of the joints to calculate the couple’s actual pose, and predict their angular acceleration in the