Several useful textbooks are available and on reserve in the Physics and Astronomy Library.
1) "Variational Principles in Classical Mechanics" by Douglas Cline. This textbook is based on the lecture notes developed by Douglas Cline while teaching P235W at the University of Rochester between 1993 - 2015. This 588-page Open Access Textbook has been published by the University of Rochester River Campus Libraries using Createspace. This textbook was developed since no single textbook covers, with the required detail, the material that was discussed in P235W. This book emphasizes the important philosophical advantages of using variational principles, rather than the vectorial approach adopted by Newton, and attempts to bridge the chasm that exists between the approaches used in classical and quantal physics. Access to free electronic copies of this book, or to order print copies from Amazon, are available at the web site: http://classicalmechanics.lib.rochester.edu/. The soft-back bound edition of this textbook is available for purchase from Amazon for $15.
2) "Classical Dynamics of Particles and Systems" 5th edition, by Thornton and Marion, (Thompson). The 5th edition is based on an excellent 1965 textbook by Jerry Marion that introduced the Lagrangian and Hamiltonian variational approaches to classical mechanics at an appropriate level for a modern junior-level mechanics course. The mathematical detail of the presentation is excellent, but the physics explanations and coverage of the philosophy underlying the variational approach are less well presented. The many worked examples presented in this book, plus the extensive set of assigned problems, are outstanding. The course content of Cline' book extends well beyond the coverage provided by this book.
3) "Classical Mechanics, 3rd edition" by Goldstein, Poole, and Safko (Addison-Wesley 1950). This is the gold standard for graduate texts in this field. This beautifully written book is more advanced than required for this course and omits worked examples that are so helpful for the neophyte classical mechanician. In spite of this, it is a valuable advanced reference since it is the only textbook that covers all the topics discussed in P235W. The 3rd edition has adopted the sophisticated symplectic notation that makes the book less friendly to undergraduates.
4) "The Variational Principles of Mechanics", 4th edition by C. Lanczos (Dover, 1949). This graduate textbook is one of the pillars of classical mechanics. It provides an excellent introduction to the philosophical aspects of the variational approach in classical mechanics. It has few worked examples and thus best serves as a secondary reference.
Several copies of the above three textbooks will be on reserve in the Physics Library.
The following textbooks also are on reserve in the Physics and Astronomy Library.
5) "Classical Mechanics" by John R. Taylor, (University Science Books). This book well matches the sequence and most of the topics taught in P235W at a similar level to Thornton and Marion. This book presents well-written, and sometimes verbose, explanations of the physics, but it contains few worked examples and the philosophy of the variational approach is not emphasized. The assigned problems are too easy and there is less mathematical detail for problem solving than in Thornton and Marion. The P235W course goes well beyond the coverage of this textbook.
6) "Classical Mechanics" by R. Douglas Gregory (Cambridge, 2006). This undergraduate textbook provides an excellent and novel introduction to classical mechanics. Unfortunately it only minimally covers the applications and modern implications included in the later parts of the P235W syllabus.
7) "Classical Mechanics, 2nd edition" Walter Greiner, (Springer, 2010). The graduate text includes a reproduction of the Struckmeier work on the extended Lagranian and Hamiltonian formalism. This excellent book includes many worked examples.
8) "Analytical Mechanics for Relativity and Quantum Mechanics, 2nd edition" Oliver Davis Johns, (Oxford Graduate Text 2011). This recent graduate text comes closest to matching the coverage of this textbook. It includes the extended Lagrangian and Hamiltonian mechanics and the Lanczos parametric model featured in the present textbook.
9) "Classical Mechanics" Morin (Cambridge) This book covers part of the required material, but it omits Hamiltonian mechanics and chaos. It does include 250 worked examples.
10) "Lagrangian and Hamiltonian Mechanics", M.G. Calkin, (World Scientific). A condensed book at a slightly more advanced level than recommended for this course.
11) "Introduction to Classical Mechanics, 2nd edition" Atam P. Arya (Prentice Hall). A text at an appropriate level for this course but does not cover all the material.
12) "Classical Mechanics" by Tai L. Chow (Wiley) This textbook is at the correct level. Unfortunately it is riddled with so many mistakes it was withdrawn by the publisher and is not recommended.
13) "Classical Mechanics and Relativity" by Harald J.W. Müller-Kirsten (World Scientific). An excellent modern graduate text that emphasizes the Theory of Relativity.