Getting Started with Taylor's Classical Mechanics
John R Taylor's Classical Mechanics is one of those books that shows up on every graduate physics reading list. It covers Lagrangian and Hamiltonian mechanics, central force problems, rigid body dynamics, and a couple chapters on chaos that aren't terrible. If you're looking for a pdf download, you'll find them scattered across various sites, but most of the links are dead or get taken down within a week. The book was published by University Science Books around 2005, and the hardcover runs roughly 950 pages. The most common place people look first is Z-Library or similar shadow libraries. Those tend to work if you can get past the initial redirect pages. Sometimes the file is in DJVU format instead of PDF, which makes it harder to read on a screen. I found a PDF copy about three years ago that had decent OCR, but the equations in the later chapters were slightly garbled. I ended up going to the university library page and downloading the DJVU version from libgen, then converting it myself with a tool called CuneiForm. That took maybe twenty minutes and saved me from misreading several derivations. One thing beginners usually miss is that Taylor assumes a solid grasp of multivariable calculus and basic vector analysis before Chapter 4. The Lagrangian chapter doesn't walk you through the calculus of variations from scratch. I ran into this when I was tutoring someone who skipped ahead. They got stuck on the Euler-Lagrange equation and couldn't figure out why the textbook seemed to pull it out of nowhere. The workaround was just going back and re-deriving one or two standard problems by hand before moving on. It took about an afternoon and made the rest of the book considerably smoother.
The section on coupled oscillators is where most people hit a wall. Taylor presents the matrix formalism quickly, and if you haven't seen eigenvalue problems in a linear algebra course, it looks like he's glossing over steps. I once spent an entire evening stuck on problem 7.14 because I'd forgotten how to diagonalize a 3x3 symmetric matrix under time pressure. The fix was just pulling up a reference on spectral decomposition and working through two warm-up examples. After that, the rest of the chapter clicked into place. There are a few known issues with certain pdf editions. Some of the scanning software merges adjacent equations, especially in the relativity chapter. If you notice a block of text that seems to contain three formulas running together, it's probably a scanning artifact. I just switched to keeping a printed copy for that chapter or using the Kindle version, which renders the equations cleanly. The Kindle version costs around forty dollars, though, so it's not free. Another edge case: the index in most pdfs is poorly formatted. Page numbers sometimes don't match the actual locations because the pagination shifts between front matter and the main text. I found it faster to just search for keywords rather than flip to the index. A quick Ctrl+F for "non-inertial frames" or "Coriolis force" gets you where you need to go in seconds.
If you need a clean copy and the shadow library routes aren't working for you, check whether your university has an institutional subscription. Many physics departments provide access through their library portal, and the downloads there are consistently higher quality. It's not the same as owning a personal copy, but it's reliable and legal.
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