Classical Mechanics

by Martin Land (Author), Lawrence P. Horwitz (Author)
This book presents classical relativistic mechanics and electrodynamics in the Feynman-Stueckelberg event-oriented framework formalized by Horwitz and Piron

It is a feature of the history of the subject that the study of atomic physics was accompanied by a partial neglect of that of classical mechanics. This led to the unsatisfactory situation in which the physicist was expected to assimilate the elements of quantum and statistical mechanics without understanding the classical foundations on which these subjects were built. The situation has improved in recent years through the general lengthening of degree courses, and it is now usual to study the analytical formulation at the late under­ graduate stage. A number of excellent treatises are available, and there are also many elementary accounts to be found in general works on physical principles. However, there has been available so far no self-contained introduction to the subject which provides the beginner with a broad general review without involving him in too much detail. It is hoped that this book may bridge the gap by pro­ viding the experimental physicist with a sufficient background for his theoretical understanding and the theorist with some stimulus to study the masterpieces of the subject. The mathematical equipment required is no more than in the normal honours physics course. For the purposes of Chapters IX­ XI it includes an elementary knowledge of cartesian tensors. A familiarity with Newtonian mechanics and some acquaintance with special relativity theory are presumed, though summarizing accounts are also given.

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 teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale.
Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics.

This textbook Classical Mechanics provides a complete survey on all aspects of classical mechanics in theoretical physics. An enormous number of worked examples and problems show students how to apply the abstract principles to realistic problems.

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.

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.