Nonlinear Dynamics and Magnetic Field Modeling in a Force-Balanced Dual-Rotor Mechanical Antenna for Compact Low-Frequency Transmitters

This paper demonstrates a dual-rotor magnetic pendulum antenna achieving record 1.61 fT magnetic field strength at 1 km through synchronized 88 Hz operation. Our approach integrates static magnetic force balance with virtualcharge-based modeling of non-uniform fields capturing statorcoil-rotor interactions. Nonlinear dynamics reveal amplitudedependent frequency shifts, while synchronized operation enables coherent field superposition. The resulting 46% field strength improvement over state-of-the-art 3-rotor systems stems from two key innovations: (1) friction-minimizing static force balance via geometric optimization and (2) field coherence enhancement through rotor synchronization. Validated by 3D-printed prototype measurements showing 66% improvement in magnetic efficiency (FOM), this work establishes a comprehensive theoretical foundation for efficient dual-rotor mechanical antennas, enabling compact low-frequency transmitters for underwater applications.