
This textbook covers all the standard introductory topics in classical mechanics, including Newton's laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity. It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.
Classical Mechanics - John R Taylor
Structure and Interpretation of Classical Mechanics - Sussman & Wisdom https://mitpress.mit.edu/books/structure-and-interpretation-...
The Theoretical Minimum - Susskind https://theoreticalminimum.com/
Introduction to Classical Mechanics - David J Morin
You can introduce Lagrangian and Hamiltonian mechanics very early on if you're okay with hand-waving over some of the analytical details and presenting it mostly as a problem solving tool. E.g. David Morin's Introduction to Classical Mechanics does a great job with minimal formal prerequisites (freshman calculus is adequate for the majority of the book) though its exercises and problems, which are the book's highlight, will be too challenging for most freshmen.
I think a low-brow problem solving centric approach is ideal as an introduction to Lagrangian mechanics in particular (not so much Hamiltonian mechanics) since the advantages are so stark and obvious compared to the Newtonian formalism. You don't have to worry about how velocities and forces transform to write down the equations of motion. You just write down the Lagrangian and take derivatives. That's something every student will immediately appreciate.
David Morin is a physics instructor at Harvard who has written several books based on his teaching:
The Green-Eyed Dragons and Other Mathematical Monsters (2018)
Special Relativity: For the Enthusiastic Beginner (2017)
Probability: For the Enthusiastic Beginner (2016)
Problems and Solutions in Introductory Mechanics (2014)
Electricity and Magnetism (2013) (revision of Purcell)
Introduction to Classical Mechanics: With Problems and Solutions (2008)