Modeling and Stability Analysis of a Sliding Bead from a Problem-Based Learning Perspective

In this work, we adopt a problem-based learning approach to develop an integrative bachelor project that relies on competences acquired from basic courses in mathematics, mechanics and computation. In this sense, the proposed project tries to pave the way from "apparently disconnected" concepts gained through previous studies toward the field of computational mechanics. On this basis, we study the motion of a particle along an arbitrary curve in space subject only to the gravitational field, the so-called sliding bead. Although this is a classic problem in mechanics, it has a substantial richness from a theoretical and practical point of view where the student reinforcing abstract skills and exploring different aspects of its numerical solution are allowed. Along this path, we start with the modeling process. This is followed by a stability analysis of the governing differential equations. Later on, we present a moderate introduction to classical numerical time integration by considering several numerical schemes and the well-known Matlab add-on Simulink. Finally, we present a brief discussion about how the proposed project allows articulating concepts of mathematics, mechanics, and computation in engineering programs of studies at horizontal and vertical levels.