PHY 520: Classical Dynamics

Topics: 

• Introduction
• Newtonian dynamics
  
• Dynamical systems with one degree of freedom
• Fixed points and limit cycles
• D'Alembert's principle
  
• Lagrangian mechanics
• Symmetries and conservation laws, Noether's theorem
  
• Hamilton's principle and calculus of variation
  
• Two-body central-force problem
• Classical scattering theory
  
• Dynamics in rotating frames of reference
• Dynamics of rigid bodies
• Oscillations
  
• Hamiltonian mechanics
• Hamilton-Jacobi theory
  
• Deterministic chaos

This course will not follow any particular textbook. Students may use any graduate text on classical dynamics for reference. Some useful texts, old ones and new ones, are listed below.

One emphasis in this course will be on the training of problem-solving skills. Exercises on specific themes will be discussed in every class. Some of the exercises will be worked out in class. Others will be assigned as homework problems (six homework problems per week with a deadline of at least one week ahead, additional problems from the list of relevant exercises with the deadline at the end of the semester).

Grade points can be earned as follows:

1. Every homework problem earns a maximum of 20 points if it is handed in before the deadline.
2. On-time class attendance earns 20 points.
3. (a) Any homework problem which is handed in after the deadline earns a maximum of 10 points. (b) Any additional problem (from the list of relevant exercises) handed in any time will earn a maximum of 5 to 20 points, depending on the degree of difficulty. (c) Any graded problem may be handed in again any time with a revised solution; additional points will be awarded for correct solutions.

Some Relevant Textbooks

• H. Goldstein: Classical Mechanics. Addison Wesley, 1981.
• I. Percival and D. Richards: Introduction to Dynamics. Cambridge University Press, 1982.
• L. D. Landau and E. M. Lifshitz: Mechanics. Pergamon Press, 1976.
• J. V. José and E. J. Saletan: Classical Dynamics: A Contemporary Approach. Cambridge University Press, 1998.
• J. L. McCauley: Classical Mechanics: Transformation, Flows, Integrable and Chaotic Dynamics. Cambridge University Press, 1997.
• D. T. Greenwood: Classical Dynamics. Dover Publications 1997.
• J. B. Kogut: Introduction to Relativity. Harcourt/Academic Press 2001.
• F. Kuypers: Klassische Mechanik, Wiley-VCH 1997.
• T. M. Helliwell and V. V. Sahakian: Modern Classical Mechanics. Cambridge University Press 2021.
  

• V. I. Arnold: Mathematical Methods of Classical Mechanics. Springer-Verlag, 1978.
• A. J. Lichtenberg and M. A. Lieberman: Regular and Stochastic Motion. Springer-Verlag, 1983.
• R. C. Hilborn: Chaos and Nonlinear Dynamics. An Introduction for Scientists and Engineers. 2nd edition. Oxford University Press 2000.
• R. C. Hilborn and N. B. Tufillaro (Eds.): Chaos and Nonlinear Dynamics. (collection of reprinted articles) AAPT Publication, 1999.
• M. Tabor: Chaos and Integrability in Nonlinear Dynamics - An Introduction. Wiley, 1989.

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