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Unformatted text preview: Preprint typeset in JHEP style  PAPER VERSION Michaelmas Term, 2004 and 2005 Classical Dynamics University of Cambridge Part II Mathematical Tripos Dr 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/dynamics.html d.tong@damtp.cam.ac.uk 1 Recommended Books and Resources L. Hand and J. Finch, Analytical Mechanics This very readable book covers everything in the course at the right level. It is similar to Goldsteins book in its approach but with clearer explanations, albeit at the expense of less content. There are also three classic texts on the subject H. Goldstein, C. Poole and J. Safko, Classical Mechanics In previous editions it was known simply as Goldstein and has been the canonical choice for generations of students. Although somewhat verbose, it is considered the standard reference on the subject. Goldstein died and the current, third, edition found two extra authors. L. Landau an E. Lifshitz, Mechanics This is a gorgeous, concise and elegant summary of the course in 150 content packed pages. Landau is one of the most important physicists of the 20th century and this is the first volume in a series of ten, considered by him to be the theoretical minimum amount of knowledge required to embark on research in physics. In 30 years, only 43 people passed Landaus exam! V. I. Arnold, Mathematical Methods of Classical Mechanics Arnold presents a more modern mathematical approach to the topics of this course, making connections with the differential geometry of manifolds and forms. It kicks off with The Universe is an Affine Space and proceeds from there... Contents 1. Newtons Laws of Motion 1 1.1 Introduction 1 1.2 Newtonian Mechanics: A Single Particle 2 1.2.1 Angular Momentum 3 1.2.2 Conservation Laws 4 1.2.3 Energy 4 1.2.4 Examples 5 1.3 Newtonian Mechanics: Many Particles 5 1.3.1 Momentum Revisited 6 1.3.2 Energy Revisited 8 1.3.3 An Example 9 2. The Lagrangian Formalism 10 2.1 The Principle of Least Action 10 2.2 Changing Coordinate Systems 13 2.2.1 Example: Rotating Coordinate Systems 14 2.2.2 Example: Hyperbolic Coordinates 16 2.3 Constraints and Generalised Coordinates 17 2.3.1 Holonomic Constraints 18 2.3.2 NonHolonomic Constraints 20 2.3.3 Summary 21 2.3.4 JosephLouis Lagrange (17361813) 22 2.4 Noethers Theorem and Symmetries 23 2.4.1 Noethers Theorem 24 2.5 Applications 26 2.5.1 Bead on a Rotating Hoop 26 2.5.2 Double Pendulum 28 2.5.3 Spherical Pendulum 29 2.5.4 Two Body Problem 31 2.5.5 Restricted Three Body Problem 33 2.5.6 Purely Kinetic Lagrangians 36 2.5.7 Particles in Electromagnetic Fields 36 2.6 Small Oscillations and Stability 38 2.6.1 Example: The Double Pendulum 41 1 2.6.2 Example: The Linear Triatomic Molecule 42 3. The Motion of Rigid Bodies 45 3.1 Kinematics 46 3.1.1 Angular Velocity 47 3.1.2 Path Ordered Exponentials 49 3.23....
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