Classical and Analytical Mechanics

jtbell Nov 9, 2017 In the US, the usual sequence is:

Undergraduate years 1-2: A broad introductory course using a single book, e.g. Halliday/Resnick. This is often two semesters (1 year) for classical physics, and one semester for “modern physics” which may be a separate book.

Undergraduate years 2-4: Intermediate-level courses using separate textbooks for each subject (e.g. Griffiths for electromagnetism, Symon for mechanics)

Graduate (MS/PhD): Advanced courses using separate textbooks again (e.g. Jackson for electromagnetism, Goldstein for classical mechanics)

Three times through the material, at increasing levels of mathematical sophistication.

Kleppner/Kolenkow is a special case in classical mechanics, sort of intermediate between the books that are usually used in the first two stages above. I think Purcell is similar for electromagnetism, although I haven’t used it myself. They’re sometimes used for fast-paced introductory courses, at places like MIT.

Nov 9, 2017 #6 Demystifier The usual process of learning physics is to first learn basics from a book such as Resnick, and then learn all this again in more detail from more specialized books. However, if the specialized books (like Kleppner which you already have) are not too difficult for you, you can skip the basics and go directly to the specialized books.

  • classical mechanics at 2nd year
  • classical electrodynamics, statistical physics and quantum mechanics at 3rd year
  • condensed matter, nuclear physics, particle physics, quantum field theory and general relativity at 4th year

Introductory Mechanics

Before tackling Kleppner, review Shankar’s’ “Fundamentals of Physics” book and online course. Here we are looking at mechanics using Newton’s original formulation.

Primary Text

An Introduction to Mechanics, 2nd Edition, Kleppner and Kolenkow, 2013

Supplementary Texts

  • Problems and Solutions in Introductory Mechanics, David Morin, 2014. “The Blue Book”
  • From David Morin’s home page: “This book (the blue book) is written for a more general audience than Introduction to Classical Mechanics (the red book). The blue-book problems are similar to the one-star and two-star problems in the red book. The red book contains many harder problems and more advanced topics. The blue book can be viewed as a stepping stone to the red book.”

Classical Mechanics

Here, in addition to looking at the Newtonian formulation in greater depth, two important alternative formulations of classical mechanics are introduced: Lagrangian mechanics and Hamiltonian mechanics.

Primary Text

Classical Mechanics, John Taylor, 2005. (Errata)

Supplementary Texts

Video Lectures

Stanford Classical Mechanics, Prof L. Susskind

Analytical Mechanics

Here the focus is exclusively on the Lagrangian and Hamiltonian-Jacobi formulations.

Primary Text

Classical Mechanics, 3rd Edition, Goldstein, Poole and Safko, 2001.

Supplementary Texts

Lecture Notes

  • David Tong: Lectures on Classical Dynamics link Lecture Notes, Professor David Tong, Cambridge University

Advanced Mechanics

Here the focus is largely on the geometric concepts underlying classical mechanics, in the language of differential geometry, symplectic geometry, differential forms, and Riemannian manifolds.

Configuration space is a differentiable manifold.

The Lagrangian \(L(q, \dot{q})\) is a real-valued function on the tangent bundle. The generalized coordinate \(q\) labels which point in the manifold and the generalized velocities \(\dot{q}\) are tangent vectors in the tangent spaces at these points.

The Hamiltonian \(H(q,p)\) is a real-valued function on the cotangent bundle. The generalized momenta \(p\) are covectors in the cotangent spaces.

Primary Text

Mathematical Methods of Classical Mechanics, 2nd Edition, V.I. Arnold, 1997

Supplementary Text