Asee peer logo

Investigation of the Transition from Order to Chaos by a Numerical Simulation of Pohl’s Wheel

Download Paper |

Conference

2019 ASEE Annual Conference & Exposition

Location

Tampa, Florida

Publication Date

June 15, 2019

Start Date

June 15, 2019

End Date

June 19, 2019

Conference Session

Engineering Physics and Physics Division Technical Session 1

Tagged Division

Engineering Physics and Physics

Page Count

18

DOI

10.18260/1-2--33025

Permanent URL

https://peer.asee.org/33025

Download Count

84

Request a correction

Paper Authors

biography

Günter Bischof Joanneum University of Applied Sciences

visit author page

Throughout his career, Dr. Günter Bischof has combined his interest in science and engineering application. He studied physics at the University of Vienna, Austria, and acquired industry experience as development engineer at Siemens Corporation. Currently he is an associate professor at Joanneum University of Applied Sciences and teaches engineering and applied mathematics.

visit author page

biography

Markus Klatzer Joanneum University of Applied Sciences

visit author page

Markus Klatzer currently works on his B.Sc. at the University of Applied Sciences in Graz. Additionally, he is part of the Formula Student racing team of his university in the section Structural Analysis and Simulation. Until obtaining his M.Sc., he intends to gain further experience by participating in the Formula Student competition. With regard to the future, he pictures himself in the high-performance sector of automotive industry.

visit author page

biography

Clemens Müller Joanneum University of Applied Sciences

visit author page

Clemens Müller currently works on his B.Sc. in automotive engineering at the FH Joanneum, University of Applied Sciences Graz, Austria. He is part of the FH Joanneum Formula Student team as an aerodynamicist and intends to work in the motorsports sector after he obtains his M.Sc.

visit author page

biography

Daniel Reifer Joanneum University of Applied Sciences

visit author page

Daniel Reifer is currently studying for a B.Sc. degree in Automotive Engineering at the Joanneum University of Applied Sciences in Graz, Austria. He joined the Formula Student racing team of his University to improve his practical skills and gained work experience as a technician in the automotive sector. On completion of his studies, he intends to pursue a career in the automotive and motorsport sector.

visit author page

biography

Christian J. Steinmann

visit author page

Christian Steinmann has an engineer degree in mathematics from the Technical University Graz, where he focused on software quality and software development process assessment and improvement. He is manager of HM&S IT-Consulting and provides services for Automotive SPiCE, ISO 15504+33000 and CMMI in the role of assessor and instructor. He performed more than 100 process assessments in software development departments for different companies in the finance, insurance, research, automotive, and automation sector. Currently, his main occupation is a consulting project for process improvement for an automobile supplier. On Fridays, he is teaching computer science introductory and programming courses at Joanneum University of Applied Sciences in Graz, Austria.

visit author page

Download Paper |

Abstract

One reason for the success of classical physics is the ability to predict the evolution of systems whose equations of motion and initial conditions are known. Unfortunately, this ability gets lost when systems behave in a chaotic way. Initially it was believed that chaotic behavior is due to the complexity of a system, but eventually it turned out that it appears even in very simple systems. Therefore it became important to gain insight into the manner of how the transition from order to chaos takes place. Now it is known that this transition follows some general patterns with which the system indicates the breakdown of the deterministic behavior.

A simple and convenient experimental setup for the investigation of such a transition between deterministic and chaotic behavior is Pohl’s wheel, a torsional pendulum named after Robert Wichard Pohl. It consists of a ring-shaped copper disk with a homogeneous mass distribution, attached to a rotation axis through its center of gravity. The wheel is elastically bound to an equilibrium position by a spiral spring. The other end of that spring is attached to a motor via an eccentric-and-rod mechanism. This motor provides an additional, external, periodic torque to the pendulum with a selectable angular frequency. Furthermore, an adjustable damping of the wheel is provided by an eddy current brake. By means of an additional mass eccentrically fixed to the wheel, which leads to an imbalance of the copper disk, the restoring force becomes nonlinear. This nonlinearity can effect chaotic behavior of the system for a certain choice of parameters.

As the search for the parameters that cause the transition into chaos turns out to be quite intricate, the experiment should be first numerically simulated and later verified in the real experimental setup. For this purpose a computer program, which simulates and visualizes the forced oscillations of Pohl’s wheel, has been developed within the framework of an undergraduate student project. The program, written in C#, offers a graphical user interface that provides a display of the moving torsional pendulum, a graph of the wheel’s deflection angle over time and a phase-space diagram. All adjustable parameters of the torsional pendulum can be modified interactively, which facilitates the identification of parameter sets leading to the transition between regular and chaotic motion.

In this paper the theoretical background, the approach to the problem and the outcome of the student project will be presented. The dynamic visual output of the program can increase and enhance the understanding of the transition of nonlinear dynamic systems into chaotic states and is therefore well suited as a teaching aid. The program is freely available and can be downloaded from our institution’s home page.

Bischof, G., & Klatzer, M., & Müller, C., & Reifer, D., & Steinmann, C. J. (2019, June), Investigation of the Transition from Order to Chaos by a Numerical Simulation of Pohl’s Wheel Paper presented at 2019 ASEE Annual Conference & Exposition , Tampa, Florida. 10.18260/1-2--33025

ASEE holds the copyright on this document. It may be read by the public free of charge. Authors may archive their work on personal websites or in institutional repositories with the following citation: © 2019 American Society for Engineering Education. Other scholars may excerpt or quote from these materials with the same citation. When excerpting or quoting from Conference Proceedings, authors should, in addition to noting the ASEE copyright, list all the original authors and their institutions and name the host city of the conference. - Last updated April 1, 2015