Stationary and libration motion in two coupled rotors: Theoretical and experimental study

Coupled dynamics of camphor rotors exhibit a rich variety of transient and stationary state phenomena. Although previous attempts at modeling these dynamics have captured some of this richness, certain observed states like rotor libration remain elusive in the models. We suggest a Coulomb-Yukawa-type potential of the form 1-e^{-Kr^{n}}/r, with n>2, where K is the strength of coupling between two rotors and r is the distance between them. The analysis proceeds by identifying fixed points and categorizing them as trivial or nontrivial. Their eigenvalues are determined to classify them as saddles or centers while varying the distance between pivots of two rotors, L. Numerical results are presented to validate the analytical findings. Additionally, libration motion is visualized with the new potential and the synchronization condition is established. The libration motion is also verified experimentally.