Students’ Understanding of Equilibrium and Stability: The Case of Dynamic Systems

Abstract

Engineering students in control courses have been observed to lack an understanding of equilibrium and stability, both of which are crucial concepts in this discipline. The introduction of these concepts is generally based on the study of classical examples from Newtonian mechanics supplemented with a control system. Equilibrium and stability are approached in different ways at the various stages of a typical engineering syllabus: at the beginning, they are mostly dealt with a static point of view, for example in mechanics, and are subsequently handled through dynamic analysis in control courses. In general, there is a little clarification of the differences between these concepts or the ways in which they are linked. We believe that this leads to much confusion and incomprehension among engineering students. Several studies have shown that students encounter difficulties when presented with simple familiar or academic static equilibrium cases in mechanics. Our study investigates students' conceptions and misconceptions about equilibrium and stability through a series of questions about several innovative nonstatic situations. It reveals that the understanding of these notions is shaken when the systems being studied are placed in inertial or non-inertial moving reference frames. The students in our study were particularly uncertain about the existence of unstable equilibrium positions and had difficulty in differentiating between the two concepts. The results suggest that students use a velocity-based approach to explain such situations. A poor grasp of the above fundamental concepts may result from previous learning experiences. More specifically, certain difficulties seem to be directly linked to a lack of understanding of these concepts, while others are related to misconceptions arising from everyday experiences and the inappropriate use of physical examples in primary school.

Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis

“…If the answer is ambiguous or has clear limitations, the modeler can repeat the cycle by considering new and more insightful observations and then improving the mathematical model. Specifically, in the retained list, the articles [4,5,8,9,12,13,17,18,20,22,48,49,54,56,58,63,65,68,74,78,88,91,94,98,100,101,115,116,118,119,127,128,130,134] are related to some approaches to the mathematical modeling for the teaching of ordinary differential equations. These works were developed between the years 2004 and 2019, with the exception of [78,130].…”

Proposal of a Mathematical Modelling Activity to Facilitate Students’ Learning of Ordinary Differential Equation Concepts

“…On the other hand, we know that the teaching of ordinary differential equations has been influenced by mathematical modelling (see [32,33,58,83,[120][121][122][123][124][125][126][127]), information and communication technologies (see [42,44,48,49,53,70,81,100,120,122,123,125,126,128]), and project-based learning (see [125,[129][130][131]) approaches. The focus of those articles is diverse.…”