Sponsored James Curry Classical Mechanics

This is a textbook on classical mechanics at the intermediate level, but its main purpose is to serve as an introduction to a new mathematical language for physics called geometric algebra. Mechanics is most commonly formulated today in terms of the vector algebra developed by the American physicist J. Willard Gibbs, but for some applications of mechanics the algebra of complex numbers is more efficient than vector algebra, while in other applications matrix algebra works better. Geometric algebra integrates all these algebraic systems into a coherent mathematical language which not only retains the advantages of each special algebra but possesses powerful new capabilities.

This upper-level undergraduate and beginning graduate textbook primarily covers the theory and application of Newtonian and Lagrangian, but also of Hamiltonian mechanics. In addition, included are elements of continuum mechanics and the accompanying classical field theory, wherein four-vector notation is introduced without explicit reference to special relativity.

This textbook takes a broad yet thorough approach to mechanics, aimed at bridging the gap between classical analytic and modern differential geometric approaches to the subject. Developed by the authors from over 30 years of teaching experience, the presentation is designed to give students an overview of the many different models used through the history of the field—from Newton to Hamilton—while also painting a clear picture of the most modern developments.

As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics.

8.01 is a first-semester freshman physics class in Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture 35), and you will be allowed a peek into the intriguing Quantum World.

The study of mechanics plays a central role in physics for a whole variety of reasons. It was one of the earliest of the quantitative sciences, and had immediate practical applications. These ranged from the study of the motion of projectiles in warfare to the motion of the planets, predicting the seasons, eclipses, etc. At the present time, even though superseded on the very small scale by quantum theory and on the very large scale by the theory of relativity, the mechanics of Newton is perfectly adequate for treating a wide spectrum of problems from the • '"etic theory of gases to the motion of space vehicles. Furthermore, the science of mechanics is regarded by many as the epitome of a good scientific theory and for this reason is studied by philosophers and social scientists alike as an exemplar of the 'scientific method'. We shall commence in Chapter 1 with a brief historical outline of the development of mechanics, mentioning the names and dates of the main participants and summarizing their contributions. Preface vii Chapter 1 Newton's laws 1. 1 Historical introduction Primitive ideas about mechanics were exemplified by the state­ ments of Aristotle (384-322 Be), who asserted that a force was necessary to maintain motion. Furthermore, he believed that there were different laws for heavenly and earthly bodies.

Many problems in classical mechanics can now be readily solved using computers. This text integrates Maple, a general-purpose symbolic computation program, into the traditional sophomore- or junior-level mechanics course. Intended primarily as a supplement to a standard text, it discusses all the topics usually covered in the course and shows how to solve problems using Maple and how to display solutions graphically to gain further insight. The text is self-contained and can also be used for self-study or as the primary text in a mechanics course.