Analytical Mechanics Books
Zulema Estabrooks
The best analytical mechanics textbook for beginners is "Classical Mechanics" by John R. Taylor. It provides a solid foundation in the principles of analytical mechanics and has clear explanations and examples that are easy for beginners to understand.
Yes, "Introduction to Analytical Mechanics" by David F. Griffiths is a highly recommended textbook for self-study. It is written in a conversational style and includes many practice problems to help readers understand the material.
The best analytical mechanics textbook for advanced students is "Analytical Mechanics" by Louis N. Hand and Janet D. Finch. It covers both classical and modern topics in analytical mechanics and is a valuable resource for graduate-level students.
Yes, there are many online resources that can supplement an analytical mechanics textbook. Some popular options include MIT OpenCourseWare, Khan Academy, and YouTube channels such as "The Organic Chemistry Tutor" and "Michel van Biezen". These resources offer video lectures, practice problems, and other helpful materials for studying analytical mechanics.
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So far at my university library, I have found many books on both subjects, but not ones with good practice questions and answers. I have Schuam's outline of Lagrangian Dynamics, but didn't really find a lot of practice questions.
Goldstein's book may be very appropriate for a first or second course on the topic, but I don't believe it displays a very formal approach to the subject. I'd suggest it to someone who's not interested in the mathematical structure of Mechanics. Even though, good for a starter.
Taylor's book has some very good exercises, but the book itself does not please me at all since it's informal, prolix and severely incomplete in most topics. Same goes to Marion's book, and even though Symon's is a little bit better, it didn't please me either.
The best book in this list if definitely Landau's, but I don't find it as good as most people picture it. I didn't read the whole Landau series (not even half, actually), but until now it's the worst of them all, for me. It still carries much of the author's incredible insights and some very nice solved exercises, but (as Arnol'd pointed out) there are a some mistakes and fake demonstrations on the book. Don't trust all of his "proofs" and you'll be safe.
Arnol'd's "Mathematical Methods of Classical Mechanics":This book is simply the best book you can get your hands on after acquiring familiarity with the subject (after a first course using Goldstein's or Landau's book, for example). It's thorough, the maths are just clear and not extravagant, the proofs are very simple and you can get some contact with phase space structures, Lie algebras, differential geometry, exterior algebra and perturbation methods. Arnol'd's way of writing is incredibly clean, as if he really wanted to write a book with no "mysteries" and "conclusions that jump out of nowhere". The exercises are not very suited for a course.
Saletan's "Classical Dynamics: a Contemporary Approach":Very nice book. A little more developed mathematically than Arnol'd's, since it delves into the structure of the cotangent bundle and spends a great deal of the book talking about chaos and Hamilton-Jacobi theory. The proofs are not very elegant, but I'd chose it as a textbook for a graduate course. Some nice exercises.
Fasano's "Analytical Dynamics":Also a graduate-textbook-style one. Very close to Saletan's way of writing, trying to explain to physicists the mathematical nature of Mechanics without too much rigor, but developing proofs of many theorems. Very nice chapter of angular momentum, very nice exercises (some of them, solved!). Incredibly nice introduction to Lie derivatives and canonical transformations, and very philosophically inclined chapters so to answer "why is this this way" or "what does that mean, really?".
Lanczos' "The Variational Principles of Mechanics":This book is kept close at all times. Not suited (at all) as a textbook, more like a companion throughout life. The most philosophical, inquiring and historical Mechanics book ever written. If you want to read a very beautiful account on the the structure, the problems, the development and the birth of mechanical concepts I'd recommend this book without blinking. It is a physics book: calculus and stuff, but looks like it were written by someone who liked to ask deep questions of the kind "why do we use this instead of this, and why is mathematics such a perfect language for physics?". It's just amazing.
Marsden's "Foundations of Mechanics":This is the bible of Mechanics. Since it's a bible, no one ever read it all or understood it all. Not to be used as textbook ever. It's a book aimed for mathematicians, but the mathematical physicist will learn a lot from it, since it's quite self contained in what touches the maths: they're all developed in the first two chapters. Even though, very acidly developed. Hard to read, hard to understand, hard to grasp some proofs... In general, hard to use. Even though, I really like some parts of if... A lot.
Kotkin's "Collection of Problems in Classical Mechanics":Last but not least, filling in the "with a lot of exercises" hole, Serbo & Kotkin's book is simply the key to score 101 out of 100 in any Mechanics exam. Hundreds of incredible, beautiful, well thought problems together with all (ALL!) their solutions at the end. From very simple to "hell no I'm not trying this one" problems, this book should be a reference to everyone studying the subject. Some of the problems are so nice that you can even publish notes in teaching journals about them, like I've seen once of twice before.
EDIT.: I just noticed I forgot one book that really changed my life: Spivak's "Physics for Mathematicians, Volume I: Mechanics". The physicist should not be scared about the title. This is the best book ever written about Mechanics. I actually have plans of taking vacations only to read it all. There's nothing missing, all the mathematics is rigorous and perfect, and there's not a single step that isn't clarified by the author (who said he was learning Mechanics himself whilst writing this book). There are moments he pauses to inquire about contact structures in symplectic manifolds, but also moments where the reason for inquiry is the fact that forces are represented by vectors; and then he goes back to Newton's time where vectors didn't exist... And tries to explain how people used to see forces and momentum at the time, in his opinion. It's just magical. He's as worried about presenting the content of the subject as to try to grasp why the definitions are the way they are, and then justify it historically. Sorry if I'm being redundant, but please read this book!
Edward A. Desloge Classical Mechanics, Vols I and II. Wiley-Interscience, 1982.The 93 chapters are remarkably short. This highly systematized and detailed book includes plenty of examples and several hundred problems, most with answers. From Newtonian mechanics it progresses to Lagrangians, Hamiltonians, and touches upon Relativity. Curiously, it is not as popular and talked about as it deserves. These two volumes belong to the bookshelf of anyone interested in learning or teaching the subject. The question was originally asked five years ago apparently by a student, perhaps today a PhD in Physics. But this reference may be useful for other students of CM.
Read Lagrange's Mécanique analytique (English translation: Analytical Mechanics). The book is split up into two parts: statics and dynamics. The first chapter, "The Various Principles of Statics," is a beautiful historical overview. Lagrange works out many problems; for example, he has a chapter entitled "The Solution of Various Problems of Statics." But, since you're interested in dynamics, you might want to focus on the second part of Analytical Mechanics.
Ok, so some of the other answers here seem like they may have forgotten what it's like to be in your position as a starting student (Goldstein as a starter book... really? Lagrange's original work?! Did you even read the question?). There are a number of great books perfectly suited to your exact position. Here are some books I think deserve consideration (I'm adding this because this question is on the community wiki, so hopefully this answer will be beneficial to at least one person in the future.):
We are now getting into the land of "second-course" books. These books may be suitable to a first course in classical mechanics, but they will probably be better as your second or third book on classical mechanics.
There are way more books on classical mechanics than what I have listed, but these are some of the best in my opinion. If you start with these, you will be ready to read any classical mechanics book you want to (barring some advanced books that are basically just symplectic geometry).
So far as I can see, there is no indication in the books' preface, colophon, etc., as to the notenooks' loccation. And the page for the book at the publisher's website, , seems to have no link whatsoever to such notebooks. (The "Downloads" link there has as target an external site giving metrics on downloads of the ebook and individual chapters of it.)
In face, as I have begun to read the book, I have not yet found any mention of Mathematica, not even in exercises in the "Mechanics" part of the book, where the preface alleges that exercises using Mathematica may be found.
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