Hamiltonian formulation with reduced variables for flexible multibody systems under linear constraints: Theory and experiment

Mechanical structures, such as robot arms in space stations and rockets that are used to support futuristic activities and carry loads in modern society, tend to be flexible owing to their reduced weight. Flexible multibody dynamics is an effective method for analyzing the dynamic motion of flexible structures. Although the Hamiltonian formulation based on the canonical theory is commonly used in multibody dynamics, certain drawbacks exist, such as complexity and computational cost. In this study, a novel flexible multibody dynamics formulation based on canonical theory is proposed with reduced variables to improve computational efficiency. This method formulates the equation of motion using only independent generalized coordinates with the assumption of linear constraint equations and the introduction of the first derivative of the constraint condition. The proposed method is combined with absolute nodal coordinate formulation and the motions of flexible structures are simulated to verify its accuracy and effectiveness. In comparison with the conventional methods, the proposed method requires less calculation time while maintaining accuracy. In addition, a wind tunnel experiment was conducted to validate the proposed method. The concurrence between the simulation and experimental results further verifies the accuracy of the proposed method.