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.

翻译：本文为受约束机械系统引入了一种端口哈密顿模型，该模型直接由拉格朗日运动方程推导得出。当前的端口哈密顿框架采用了一种无奇异的刚体旋转导向矢量表示，从而得到恒定的质量矩阵。研究表明，端口哈密顿刚体子系统的功率保持互联在数学上等价于使用运动副描述理想关节的经典方法。这建立了一个与传统建模范式一致的端口哈密顿多体动力学框架。值得注意的是，所导出的指标-2微分代数方程组的端口哈密顿结构，使得应用隐式、结构保持的中点时间积分成为可能。所提出的方案能够同时满足总能量与角动量的平衡定律以及位置级约束。这些特性使得所提方法具有显著的鲁棒性，并能实现稳定的长期仿真。此外，本文还纳入了一种基于变分原理推导的指标约简策略，该策略在保持端口哈密顿结构的同时，除了位置级约束外还能强制执行速度级约束。数值算例展示了所提表述的优良特性，该表述非常适用于基于能量的控制设计。