Abstract

This study investigates the Tennis Tacket Flip, a dynamic instability where small perturbations in angular velocity grow to induce rotations about all three principal axes; rotations that repeat periodically. Previous work has explored the role of off-axis perturbations in angular velocity. This work explores the role of eccentric mass distributions that render the mass moment of inertia matrix non-diagonal. Leveraging a gyroscope, we experimentally test this assumption, confirming theoretical predictions. Alongside, we summarized Emmy Noether's foundational work on conservation laws as an alternative to the Newtonian approach. This was done to make her work accessible to undergraduates to inspire students. Continuing, while previous work has demonstrated that the intersection of the energy sphere and angular momentum ellipsoid does predict the flip, this project extends that without delving into these details. Our findings validate the dynamics of the Tennis Racket Flip under both induced perturbation conditions – one of angular velocity kinematics versus one of eccentric mass kinetics. This validation was through numerical simulation and a physical experiment. This paper will report on the varied aspects involved: the mathematics of Noether, the mathematics of the flip, the coding using Runge-Kutta, and the manufacturing of the gyroscopic device.

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