Classical Mechanics null Edition
Book Preface
This book is intended for students of the physical sciences, especially physics, who have already studied some mechanics as part of an introductory physics course (“freshmanphysics” at a typical American university) and are now ready for a deeper look at the subject. The book grew out of the junior-level mechanics course which is offered by the Physics Department at Colorado and is taken mainly by physics majors, but also by some mathematicians, chemists, and engineers. Almost all of these students have taken a year of freshman physics, and so have at least a nodding acquaintance with Newton’s laws, energy and momentum, simple harmonic motion, and so on. In this book I build on this nodding acquaintance to give a deeper understanding of these basic ideas, and then go on to develop more advanced topics, such as the Lagrangian and Hamiltonian formulations, the mechanics of noninertial frames, motion of rigid bodies, coupled oscillators, chaos theory, and a few more.
Mechanics is, of course, the study of how things move — how an electron moves down your TV tube, how a baseball flies through the air, how a comet moves round the sun. Classical mechanics is the form of mechanics developed by Galileo and Newton in the seventeenth century and reformulated by Lagrange and Hamilton in the eighteenth and nineteenth centuries. For more than two hundred years, it seemed that classical mechanics was the only form of mechanics, that it could explain the motion of all conceivable systems.
Then, in two great revolutions of the early twentieth century, it was shown that classical mechanics cannot account for the motion of objects traveling close to the speed of light, nor of subatomic particles moving inside atoms. The years from about 1900 to 1930 saw the development of relativistic mechanics primarily to describe fastmoving bodies and of quantum mechanics primarily to describe subatomic systems. Faced with this competition, one might expect classical mechanics to have lost much of its interest and importance. In fact, however, classical mechanics is now, at the start of the twenty-first century, just as important and glamorous as ever. This resilience is due to three facts: First, there are just as many interesting physical systems as ever that are best described in classical terms. To understand the orbits of space vehicles and of charged particles in modern accelerators, you have to understand classical mechanics. Second, recent developments in classical mechanics, mainly associated with the growth of chaos theory, have spawned whole new branches of physics and mathematics and have changed our understanding of the notion of causality. It is these new ideas that have attracted some of the best minds in physics back to the study of classical mechanics. Third, it is as true today as ever that a good understanding of classical mechanics is a prerequisite for the study of relativity and quantum mechanics.
Physicists tend to use the term “classical mechanics” rather loosely. Many use it for the mechanics of Newton, Lagrange, and Hamilton; for these people, “classical mechanics” excludes relativity and quantum mechanics. On the other hand, in some areas of physics, there is a tendency to include relativity as a part of “classical mechanics”; for people of this persuasion, “classical mechanics” means “non-quantum mechanics.” Perhaps as a reflection of this second usage, some courses called “classical mechanics” include an introduction to relativity, and for the same reason, I have included one chapter on relativistic mechanics, which you can use or not, as you please.
An attractive feature of a course in classical mechanics is that it is a wonderful opportunity to learn to use many of the mathematical techniques needed in so many other branches of physics — vectors, vector calculus, differential equations, complex numbers, Taylor series, Fourier series, calculus of variations, and matrices. I have tried to give at least a minimal review or introduction for each of these topics (with references to further reading) and to teach their use in the usually quite simple context of classical mechanics. I hope you will come away from this book with an increased confidence that you can really use these important tools.
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