A novel and efficient Hamiltonian dynamic analysis approach for constraint force determination in flexible multibody systems

Abstract

In the dynamic analysis of flexible multibody systems, Hamiltonian formulations offer advantages in numerical stabilization and systematic handling of systems with varying mass. However, current approaches face challenges. Differential algebraic equations (DAEs) can directly express constraint forces but are computationally inefficient, while ordinary differential equations (ODEs) are more computationally efficient but cannot directly represent constraint forces due to the elimination of the Lagrange multiplier. This paper presents an innovative and efficient dynamic analysis approach based on the Hamiltonian formulation, incorporating velocity transformation and open-constraint coordinate methods. Compared to conventional DAE-based Hamiltonian formulations, our approach conducts analysis efficiently using only independent variables. Compared to conventional ODE-based Hamiltonian formulations, our approach effectively expresses constraint forces through Lagrange multiplier reformulation. Furthermore, when compared to the traditional ODE-based Lagrangian formulation, our approach exhibits superior computational efficiency. Numerical simulations assess our proposed formulation, showing agreement with conventional formulations, shorter calculation time, and alignment with analytical results, confirming the accuracy and usefulness of our approach.