🤖 AI Summary
This work addresses the challenge of preserving energy structure and ensuring long-term stability in multibody dynamics simulations by proposing a port-Hamiltonian framework equivalent to the classical ideal joint model. Built upon Lagrange’s equations, the approach employs singularity-free directional vectors to represent rigid body rotations, incorporates variational principles for index reduction, and solves the resulting index-2 differential-algebraic equations using a structure-preserving midpoint integrator. The resulting model rigorously satisfies both position- and velocity-level constraints while exactly conserving total energy and angular momentum. This exact preservation significantly enhances the accuracy and stability of long-duration simulations and provides a solid theoretical foundation and numerical advantage for energy-based control design.
📝 Abstract
This work introduces a port-Hamiltonian (PH) model for constrained mechanical systems, which is directly derived from the Lagrangian equations of motion. The present PH framework incorporates a singularity-free director representation of rigid body rotations, resulting in constant mass matrices. It is shown that the power-preserving interconnection of PH rigid-body subsystems is mathematically equivalent to the classical description of ideal joints using kinematic pairs. This establishes a PH multibody dynamics framework that is consistent with traditional modeling paradigms.
Notably, the PH structure of the governing index-2 differential-algebraic equations enables the application of an implicit, structure preserving midpoint time integration. The proposed scheme is able to satisfy both the balance laws for total energy and angular momentum as well as the position-level constraints. These properties make the proposed method remarkably robust and enable stable long-term simulations. Furthermore, a variationally derived index-reduction strategy is incorporated that enforces velocity-level constraints in addition to position-level constraints while preserving the port-Hamiltonian structure. Numerical examples illustrate the favorable properties of the proposed formulation, which is well-suited for energy-based control design.