On the efficacy of pseudo-coordinates—Part 1: moving interior constraints

Abstract

In a recent publication, a Gibbs–Appell type projection methodology for modeling non-holonomic hybrid parameter multiple body systems (HPMBS) was presented. In this methodology, pseudo-coordinates and pseudo-speeds were introduced felicitously into the kinematic chain to allow rigorous inclusion of holonomic or non-holonomic constraints that occur among the hybrid parameter bodies; including intra-domain constraints applied within distributed parameter bodies in the system. In this paper, a HPMBS that exhibits intra-domain holonomic constraints and is, for comparison purposes, analytically tractable by hand via Hamilton's principle is studied. The purpose of this comparison and study is to evince the utility and effectiveness of the pseudo-variable based technique. This is accomplished by demonstrating the novel and judicious use of pseudo-coordinates and speeds in modeling HPMBS. It is shown, by allowing the natural description of the kinematic chain (open or closed) to be manifested with the natural pseudo-coordinates and speeds, that low-order models can accurately describe the dynamics of complicated HPMBS. Thus, the trend of ever-increasing degrees of freedom in the modeling of complicated flexible systems is also shown to be unnecessary, provided the proper natural finesse is applied.