Dynamic Behavior of a Two‐Degree‐of‐Freedom System With Electromagnetic Interaction via a Skew‐Symmetric Matrix

ABSTRACT This paper analyzes the dynamic behavior of a two‐degree‐of‐freedom system subjected to electromagnetic interaction modelled through a skew‐symmetric coupling matrix. The system comprises two mechanically independent oscillators coupled by velocity‐dependent electromagnetic forces. The equations of motion are formulated and analyzed in the modal domain, highlighting the effects of the antisymmetric interaction on natural frequencies and mode shapes. The classical orthogonality is broken, resulting in complex eigenvectors; nevertheless, the system remains conservative, as the interaction forces perform no work. The analysis is carried out using both configuration‐space and state‐space formulations, revealing modal frequency splitting and phase shifts induced by the skew‐symmetric term. These modal features are further examined through time‐domain simulations and frequency response functions. The main contribution of this study is the development and analysis of a deliberately simple yet general model that isolates the essential dynamic effects of skew‐symmetric electromagnetic coupling. This minimal formulation, often hidden in more complex systems, reveals key phenomena such as modal frequency splitting, non‐normal modes, and energy‐conserving cross‐effects. The model serves not only as a conceptual reference but also as a methodological framework applicable to a broad class of coupled electromechanical systems.