Classical Mechanics

Citation

Taylor, J. R. (2005). Classical Mechanics. University Science Books.

Chapter Summary

The book runs to about 790 pages in two parts: eleven chapters of "Essentials" and five chapters of "Further Topics", followed by a single mathematical appendix. Every chapter ends with a set of problems.

Chapters 1–4: Newton's Laws of Motion; Projectiles and Charged Particles; Momentum and Angular Momentum; Energy

The opening chapters revisit Newtonian mechanics beyond the introductory level: Newton's laws, motion of projectiles and of charged particles in fields, and the conservation laws for momentum, angular momentum and energy.

Chapter 5: Oscillations

H. R. Harrison's review identifies the chapter on vibration as the place where viscous damping enters, for systems with a single degree of freedom, in a book whose examples are otherwise mostly frictionless.

Chapters 6–7: Calculus of Variations; Lagrange's Equations

Variational methods arrive early, in the middle of Part I: the calculus of variations (Chapter 6) comes immediately before Lagrange's equations (Chapter 7), so Lagrangian methods are available for the rest of Part I.

Chapters 8–9: Two-Body Central Force Problems; Mechanics in Noninertial Frames

Chapter 8 covers the two-body problem under a central force, the setting for orbits. Chapter 9 treats motion described from accelerating and rotating frames; Harrison's review mentions a treatment of tides among its examples.

Chapters 10–11: Rotational Motion of Rigid Bodies; Coupled Oscillators and Normal Modes

Part I closes with the rotation of rigid bodies and with coupled oscillators and normal modes. The book's single appendix, on diagonalizing real symmetric matrices, covers the matrix technique on which principal axes and normal modes rely.

Chapter 12: Nonlinear Mechanics and Chaos

The first of the further topics. The publisher singles it out as a highlight, describing it as built around a few simple systems so that the central ideas of chaos are accessible.

Chapters 13–14: Hamiltonian Mechanics; Collision Theory

Chapter 13 introduces the Hamiltonian formulation as an alternative to the Lagrangian one; Chapter 14 treats collisions.

Chapter 15: Special Relativity

Harrison found this chapter clear and concise while still covering the main concepts of the theory.

Chapter 16: Continuum Mechanics

The book ends with an introduction to continuum mechanics, the only chapter that moves from particles and rigid bodies to extended deformable media.

Key Concepts

Part I: Essentials (Chapters 1–11)

• Conservation laws: momentum, angular momentum and energy, the principles the opening chapters build on.
• Calculus of variations: finding the path that makes an integral stationary, the mathematics behind Lagrangian mechanics.
• Lagrange's equations: equations of motion derived from a single function of generalized coordinates and velocities, convenient for constrained systems.
• Noninertial frames: describing motion from accelerating or rotating frames, where fictitious forces appear.
• Normal modes: the independent patterns of oscillation of a coupled system, found by diagonalizing a symmetric matrix.

Part II: Further Topics (Chapters 12–16)

• Chaos: sensitive, unpredictable long-term behaviour of deterministic nonlinear systems.
• Hamiltonian mechanics: a formulation of mechanics in terms of coordinates and momenta.
• Special relativity: the mechanics of bodies moving at speeds comparable to that of light.
• Continuum mechanics: the mechanics of extended, deformable media.

Critical Analysis

Strengths

• Clarity of writing. Harrison, reviewing the book in The Aeronautical Journal (April 2005), wrote that despite its length it is not heavy reading and that the presentation is clear enough to suggest a capable lecturer in the room. A review quoted by the publisher and attributed to the American Journal of Physics judged it far more readable than the two texts then most used for the course, Fowles (which, it said, students find too terse) and Marion and Thornton (which they find too wordy).
• A large, graded problem set. The publisher gives 744 end-of-chapter problems, classified by topic and approximate difficulty and ranging from simple exercises to computer projects. Harrison adds that the chapters contain many worked examples and that answers are given to half of the problems; a separate Student Solutions Manual is available.
• Lagrangian methods early. The calculus of variations and Lagrange's equations come at Chapters 6–7, before central forces, noninertial frames, rigid bodies and normal modes, so the second half of Part I can use the Lagrangian approach throughout.
• Accessible further topics. The publisher highlights the chaos chapter's focus on a few simple systems, and Harrison praised the special relativity chapter. Part II gives a course a choice of extensions.
• A structure that maps cleanly onto a semester. The split between "Essentials" and "Further Topics" is how courses actually use the book. The Lehigh course listed under Common course assignments, for example, requires Chapters 1–11 and adds Chapters 12 and 13 only if time permits, which is exactly the Part I core plus optional extensions.

Limitations

• Long. At about 790 pages the book holds more than one semester of material, and Harrison calls it a long book; courses must choose among the Part II chapters. The two courses listed below choose differently: Lehigh treats Chapters 12–13 as optional, while Maryland covers Chapters 1–15 but leaves out Chapter 12. Readers working alone should expect to make a similar choice.
• Physics-centred applications. Harrison notes that the applications come mainly from fundamental physics and that most examples ignore friction: viscous damping appears only for single-degree-of-freedom vibration, and the two- and three-degree-of-freedom systems are undamped. Engineering students will need other sources for dissipative systems.
• Specific points questioned by a reviewer. Harrison reported what he considered a fundamental error in the example of a block sliding down a plane with dry friction (presented as a work–energy example but, in his reading, solved by integrating the equation of motion), and called the tidal example odd for treating the Earth–Moon system as linearly accelerating rather than orbiting. These two examples are worth reading critically.

Where It Fits in the Course

Taylor is the natural main text in this course list for a second-year or third-year course in classical mechanics. It is used that way in practice: both courses described under Common course assignments list it as the course textbook. Two more elementary books come before it in different ways. Chabay and Sherwood's Matter and Interactions is a calculus-based introductory course built on the momentum principle and simple computation, the kind of first-year mechanics Taylor assumes. Susskind and Hrabovsky's The Theoretical Minimum is a compact, lecture-based tour from Newton's laws to Lagrangian and Hamiltonian ideas that can serve as a preview of Chapters 6–7 and 13.

David Morin's Introduction to Classical Mechanics covers similar ground with a large collection of problems and detailed solutions, which makes it a good source of further practice alongside or after Taylor. Goldstein, Poole and Safko's Classical Mechanics is the graduate-level treatment of the Lagrangian and Hamiltonian formulations and is the usual next step after Taylor's Chapters 7 and 13. Students whose course stops at Chapter 11, as the Lehigh course's required list does, may meet the Hamiltonian formulation for the first time in Goldstein and should read Taylor's Chapter 13 first. Alexander Smits's A Physical Introduction to Fluid Mechanics continues where Taylor's single chapter on continuum mechanics stops.

How to Use This Book

The publisher describes the book as intended for students who have studied some mechanics in an introductory physics course, such as "freshman physics"; readers should be comfortable with calculus, and the appendix covers the matrix diagonalization used for normal modes. It suits physics majors in the second or third year and engineering or mathematics students who want a careful introduction to variational mechanics.

A practical plan for a one-semester course:

• Core: Part I in order. Chapters 1–4 can move quickly for students with a strong introductory course, but should not be skipped, since the conservation laws they cover underpin everything after. Chapters 5–7 are the heart of the course: oscillations, then the calculus of variations and Lagrange's equations.
• Applications of the core: Chapters 8–11 (central forces, noninertial frames, rigid bodies, normal modes); the appendix on diagonalizing symmetric matrices is relevant to the last two.
• Further topics: choose one or two Part II chapters to match the course: Chapter 13 for students heading to quantum mechanics, Chapter 12 for a computational emphasis, Chapter 15 if relativity is not taught elsewhere. A Part II chapter also makes a good term project.

Use the difficulty classification to pick problems: a few of the easier ones on each topic to check understanding, then a smaller number of harder ones. Try at least some computer problems, especially with the chaos chapter. Because answers are given for only half of the problems, check the others with a classmate, by limiting cases or with the Student Solutions Manual.

Common course assignments

Published syllabi show how instructors divide the book:

• Lehigh PHY 215 Classical Mechanics, Spring 2024. The textbook is Taylor's Classical Mechanics (University Science Books). Chapters 1–11 are the required topics, and Chapters 12 (nonlinear mechanics and chaos) and 13 (Hamiltonian mechanics) are covered if time permits. This is the clearest recent model for a one-semester course and matches the plan above: all of Part I, then one or two Part II chapters.
• University of Maryland Physics 410 (Chacko), undated. The syllabus covers Chapters 1 through 15 but leaves out Chapter 12. That means Hamiltonian mechanics, collision theory and special relativity are included and chaos is dropped. The PDF gives no term or year, so it may not reflect current practice.

Neither syllabus includes Chapter 16. Maryland omits Chapter 12, while Lehigh lists Chapters 12 and 13 as optional if time permits. A self-studying reader who wants Lagrangian and Hamiltonian mechanics for later courses can follow the Maryland sequence. A reader interested in nonlinear dynamics should take up Chapter 12 deliberately, since a course may not reach it.

Edition identity and preparation

University Science Books lists the print edition, ISBN 9781891389221, with a 2005 publication date, while the current distributor, MIT Press, gives a September 2004 release; this guide cites the 2005 date. In the edition listed here, the table of contents places energy in Chapter 4, oscillations in Chapter 5, and variational and Lagrangian methods in Chapters 6–7, and the course assignments above use the same chapter numbering. If force diagrams are still unfamiliar, an algebra-based introductory text is a better preparation than beginning with the variational chapters.