Dynamics and Dynamical Systems


The intended audience for this book are first-year college students majoring in science or engineering. It is expected from the student to have some basic knowledge of Linear Algebra and Calculus. The development of personal computers has expanded the type of problems that can be solved by a student in an introductory Physics course. Computational and simulation programs allow the student to understand the concepts involved in a physics problem even before he learns the analytic methods to solve it. The computational methods introduced to solve mechanics problems have been extended into other areas outside of physics, giving rise to the general theory of dynamical systems.

This book aims at giving the reader some basic knowledge of mechanics and the computational techniques used to solve dynamical systems. The Computer Algebra System (CAS) Maxima is used to introduce those computational techniques. The main theme of the book is mechanics, including some contemporary subjects such as nonlinear systems and chaos. The approach used is that of Classical Mechanics, in which time and space are assumed to be absolute and independent from the observers.

This book was originally written in Portuguese, as a textbook for the course Physics 1 (EIC0010) from the first-year curriculum of the "Masters in Informatics and Computing Engineering" program (MIEIC) at the Faculty of Engineering of the University of Porto and it is the first volume in a series of two. The second volume is "Electricity, Magnetism and Circuits" (Villate, 2014). This book and its additional material are updated frequently and it can be found at the site Dinamics and Dynamical Systems.

The course for which this textbook was written consists of 12 weeks of classes with 2 one-hour lectures and a two-hour practical session every week. The practical sessions are held in a room with laptop computers that the students can use to access the course and other websites and to run Maxima.

The first six chapters follow the program that is traditionally taught in an introductory mechanics course, without including many-body systems or fluid mechanics. Chapter 7 is an introduction to dynamical systems. Chapter 8 is about lagrangian mechanics and chapters 9, 10 11 and 12 are about dynamical systems.

I thank Professor João Rui Guedes de Carvalho who made a careful review of the Portuguese version and with whom I had some useful discussions about mechanics and teaching methods. I would also like to acknowledge the valuable help of my students, whose enthusiasm and thirst for knowledge have been my inspiration to write this book. There have been many students throughout the years who have pointed out typos and confusing parts, thus helping me to improve the text. I also thank the instructors who taught some of the practical lectures of the course during the years when I wrote the first versions of the book, Maria Helena Braga, Francisco Salzedas and Helder Silva. Finally, I thank my graduate student João Carvalho who not only assisted me with the practical sessions, but also shared with me his knowledge of the Physics of Sports from his experience as an athlete.

Jaime E. Villate
E-mail: villate@fe.up.pt
Porto, February of 2016