Numerical approaches for constraint stabilization of constrained dynamic system

Abstract

Numerous studies have explored constrained motion within structural and mechanical systems, revealing that numerical integrations of such dynamic responses often exhibit drift errors, diverging from intended trajectories. This study introduces two numerical analysis techniques aimed at mitigating these errors. In 1992, Udwadia and Kalaba introduced the Generalized Inverse Method (GIM), providing a unique, explicit mathematical formulation for describing constrained motion. This paper presents a Modified Generalized Inverse Method (MGIM) that refines the GIM by adjusting the coefficients at the acceleration level constraints. Additionally, a Direct Integration Method (DIM) is developed by minimizing the discrepancy between unconstrained and constrained accelerations, incorporating coefficients into acceleration level constraints. Numerical examples demonstrate that the magnitude of these coefficients significantly influences drift errors. Moreover, it is shown that constrained responses can be stabilized and errors reduced, although this study does not specify the exact coefficients necessary for achieving stabilization.