Mathematical Modeling of the Dynamics of a System with n Bodies Mounted on Two Elastic Beams

The article presents the derivation of a mathematical model for a mechanical system consisting of n bodies mounted on two elastic beams. The Hamilton–Ostrogradsky variational principle is applied to derive the equations of motion, which are obtained in a generalized form. This study continues a series of previous works devoted to the analysis and modeling of hybrid systems of differential equations that describe the behavior of mechanical systems with complex structures. The main novelty of the research lies in considering the case of mounting bodies on two beams, which expands the class of models under investigation and allows for the inclusion of additional interaction factors between the system's components. The developed model accounts for elastic deformations of the beams, their mutual influence, and the dynamic behavior of the bodies. The results obtained can be used for stability analysis and optimization of similar systems in engineering applications.