No-Nonsense Classical Mechanics: A Student-Friendly Introduction

Book Preface

Classical mechanics is more than 300 years old and dozens, maybe even hundreds, of textbooks on the subject have already been written. So why another one?
First of all, this book focuses solely on the fundamental aspects of classical mechanics.1 This narrow focus allows us to discuss 1 Applications are only discussed insofar as they help to deepen our understanding of the fundamental concepts and not as an end inthemselves. In addition, there are already dozens of great books which discuss applications or other special topics in great detail. Some of the best ones are recommended in Chapter 13. all of the important concepts several times from various perspectives.

In contrast, most other classical mechanics textbooks try to do a lot at once. For example, it’s not uncommon that in addition to the Newtonian, Lagrangian and Hamiltonian formulations, dozens of applications, edge cases, advanced topics, historical developments or even biographies of the most important contributors are discussed. I think this is problematic because, as the saying goes, if you try to be good at everything, you will not be great at anything.

So a clear advantage of the approach used in this book is that the reader has multiple chances to understand a given concept, while in a “normal” textbook the reader immediately has a problem when a passage is not understood perfectly.2 A second 2 In a “normal” textbook, each topic is only introduced once. As a result, later chapters become harder and harder to understand without a full understanding of all previous chapters. Moreover, it’s easy to become discouraged when a few passages are not perfectly clear since you know that you need the knowledge to understand later chapters. advantage of our narrow focus is that it minimizes the risk of unnecessarily confusing the reader. Like all other fundamental theories, classical mechanics is, at its heart, quite simple. However, using it to describe complicated systems is far from easy and this is where most of the difficulties usually arise.3 3 Most of the difficulties are really mathematics problems, not physics problems anyway, e.g., solving a difficult integral or solving a given differential equation.

In summary, restricting ourselves to the fundamentals allows us to introduce classical mechanics as gently as possible. 4 While advanced applications are, 4 of course, important, they are not essential to understand the fundamentals of classical mechanics.
There are many great books which focus on specific applications. After you’ve developed a solid understanding of the fundamentals, it’s far easier to learn more about those applications you’re really interested in.

While this alone may already justify the publication of another classical mechanics textbook, there are a few other things which make this book different:
� Firstly, it wasn’t written by a professor. As a result, this book is by no means an authoritative reference. Instead, this book is written like a casual conversation with a more experienced student who shares with you everything he wishes he had known earlier. I’m convinced that someone who has just recently learned the topic can explain it much better than someone who learned it decades ago. Many textbooks are hard to understand, not because the subject is difficult, but because the author can’t remember what it’s like to be a beginner5. 5 This is known as the “Curse of Knowledge.”
� Secondly, this book is unique in that it contains lots of idiosyncratic hand-drawn illustrations. Usually, textbooks include very few pictures since drawing them is either a lot of work or expensive. However, drawing figures is only a lot of work if you are a perfectionist. The images in this book are not as pretty as the pictures in a typical textbook since I firmly believe that lots of non-perfect illustrations are much better than a few perfect ones. The goal of this book, after all, is to help you understand classical mechanics and not to win prizes for my pretty illustrations.
� Finally, my only goal with this book was to write the most student-friendly classical mechanics textbook and not, for example, to build my reputation. Too many books are unnecessarily complicated because if a book is hard to understand it makes the author appear smarter.6 To give a concrete ex- 6 To quote C. Lanczos: “Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman.” ample, nothing in this book is assumed to be “obvious” or “easy to see”. Moreover, calculations are done step-by-step and are annotated to help you understand faster.

Without any further ado, let’s begin. I hope you enjoy reading this book as much as I have enjoyed writing it. Karlsruhe, June 2018 Jakob Schwichtenberg
PS: I regularly incorporate reader feedback. So if you find an error or have any other kind of comment, I would appreciate an email to [email protected].

Acknowledgments
Special thanks to Dr. Florian Colbatzky whose comments, ideas and corrections have made this book so much better. I also want to thank Michael Havrilla, Hywel Griffiths, Daniel Thomas Speckhard, Alex Huang, Eduard Sackinger, Mark Sacchetti, Ronnie Webb, Stephan Lange, Alexandre Felix, Luis Arias and Fabian Waetermans for reporting several typos and to Dena Russell and Jacob Ayres for carefully proofreading the manuscript