A Generalized Inertia Representation for Rigid Multibody Systems in Terms of Natural Coordinates

The paper aims to investigate the appropriate Inertia Representation (IR) stemming from natural coordinates that is computationally efficient for rigid multibody systems with holonomic constraints. To this end, we develop the Generalized Inertia Representation (GIR) that results in a two-parameter family of formulations for the mass matrix. By properly selecting the parameters, the GIR includes the IRs of the Classical Natural Coordinates (CNC), the Natural Absolute Coordinates (NAC), and the Reference Point Coordinates featuring the Convected Base Vectors (RPC-CBV), etc. It is found that the parameters in the GIR influence the discretization error. Therefore, a parameter-preadjusting approach is proposed to improve the numerical accuracy of integrations. Comprehensive comparisons of numerical performances under the framework of the GIR are carried out using the variational integrator. We show that the GIR with preadjusted parameters achieves higher accuracy than other IRs. To achieve the same level of accuracy, the GIR requires fewer computations than the traditional IR of the CNC or the NAC. Therefore, the GIR with preadjusted parameters is preferred for long-time simulations of multibody systems, where the cost of preadjusting can be ignored.