Lent Term, 2013

Dynamics and Relativity

University of Cambridge Part IA Mathematical Tripos

David Tong

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 OBA, UK http://www.damtp.cam.ac.uk/user/tong/relativity.html d.tong@damtp.cam.ac.uk

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Recommended Books and Resources

• Tom Kibble and Frank Berkshire, “Classical Mechanics” • Douglas Gregory, “Classical Mechanics” Both of these books are well written and do an excellent job of explaining the fundamentals of classical mechanics. If you’re struggling to understand some of the basic concepts, these are both good places to turn. • S. Chandrasekhar, “Newton’s Principia (for the common reader)” Want to hear about Newtonian mechanics straight from the horse’s mouth? This is an annotated version of the Principia with commentary by the Nobel prize winning astrophysicist Chandrasekhar who walks you through Newton’s geometrical proofs. Although, in fairness, Newton is sometimes easier to understand than Chandra. • A.P. French, “Special Relativity” A clear introduction, covering the theory in some detail. • Wolfgang Pauli, “Theory of Relativity” Pauli was one of the founders of quantum mechanics and one of the great physicists of the last century. Much of this book was written when he was just 21. It remains one of the most authoritative and scholarly accounts of special relativity. It’s not for the faint of heart. (But it is cheap). A number of excellent lecture notes are available on the web. Links can be found on the course webpage: http://www.damtp.cam.ac.uk/user/tong/relativity.html

Contents

1. Newtonian Mechanics 1.1 Newton’s Laws of Motion 1.1.1 Newton’s Laws 1.2 Inertial Frames and Newton’s First Law 1.2.1 Galilean Relativity 1.3 Newton’s Second Law 1.4 Looking Forwards: The Validity of Newtonian Mechanics 1 2 3 4 5 7 9

2. Forces 10 2.1 Potentials in One Dimension...

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