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

Area of Science:

• Physics
• Chemical Physics
• Nonlinear Dynamics

Background:

• Camphor rotor dynamics exhibit complex transient and stationary states.
• Existing models struggle to replicate phenomena like rotor libration.

Purpose of the Study:

• To develop a novel potential model for camphor rotor dynamics.
• To accurately capture elusive states such as rotor libration.
• To establish synchronization conditions and validate findings experimentally.

Main Methods:

• Proposed a Coulomb-Yukawa-type potential: 1-e^{-Kr^{n}}/r, with n>2.
• Identified and categorized fixed points (trivial/nontrivial).
• Analyzed eigenvalues to classify fixed points (saddles/centers) by varying inter-rotor pivot distance (L).
• Utilized numerical simulations for validation.
• Visualized libration motion and established synchronization conditions.

Main Results:

• The new potential successfully models camphor rotor dynamics, including libration.
• Analytical findings were validated through numerical results.
• Synchronization conditions for libration were determined.
• Experimental verification confirmed the model's accuracy.

Conclusions:

• The proposed Coulomb-Yukawa-type potential provides a more comprehensive description of coupled camphor rotor dynamics.
• The model accurately predicts and explains rotor libration, a previously elusive phenomenon.
• The study bridges analytical, numerical, and experimental approaches to understand complex rotor systems.