The aim of this study is to investigate the bouncing dynamics of a small elastic ball on a rectangular stairway and to determine if its dynamics is chaotic. We derive a simple nonlinear recursion for the coordinates of the collisions from which the type of dynamics cannot be predicted. Numerical simulations indicate that stationary bouncing always sets in asymptotically, and is typically quasi-periodic. The dependence on the coefficient of restitution can be very complicated, yet the dynamics is found to be nonchaotic. Only elementary mathematics is required for the calculations, and we offer a piece of userfriendly demo software on our website, http://crnl.hu/stairway, to facilitate further understanding of this complex phenomenon.
We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball), as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.