Classical Mechanics

FYTN09, 7.5 ECTS

Spring 2012

The official home page for the course is at
http://www.thep.lu.se/english/education/courses/classical_mechanics/

• General Information

  This is a 7.5 hp Master/PhD course in Theoretical Physics at Lund University with the main focus on basic concepts and applications of classical mechanics. The course is scheduled for the first part of the semester (January 17 to March 20).

• Introduction meeting

  Tuesday 17 January 2012, 10.15, room NB, basement theoretical physics (basement theoretical physics, K262, house K, Sölvegatan 14A).

• Course Contents

  This course gives a solid basis in classical mechanics in its Lagrangian and Hamiltonian formulation, with connections to modern physics.

  For more detailed information see below

  Formal description of the course (in Swedish) (official course plan)

• Prerequisites

  Rigorous junior-level knowledge in mechanics, calculus and linear algebra is required.

• Literature

  Course book: Goldstein, Poole and Safko, Classical Mechanics, third edition, Addison Wesley, 2001

  There are many misprints in the book. http://astro.physics.sc.edu/Goldstein has a list of them.

• Schedule

  Lectures will take place on Monday's and Friday's at 10.15-12.00 (room NB) and on Wednesday's at 13.15-15.00 (room HUB) unless noted otherwise. The course will consist of approximately 20 lectures (2x45min) and 5 problem solving sessions. There will be four homework assignments, each has to be prepared by the following problem solving session, where those will be thoroughly discussed in the class. It is recommended to have the problems solved more or less simultaneously with studying the corresponding chapters. But it is strongly recommended to attend a corresponding lecture first.

  Date	Time	Place	Subject	Goldstein's sections	Problems
  Tue 17/1	10-12	Sal NB	Introduction. D'Alembert principle and Lagrangian.	1.1-1.5	Exercises 1.1,1.5,1.8,1.16
  Wed 18/1	10-12	Sal NB	Hamilton's principle. Conservation theorems.	2.1,3,4,6,7	Exercises 2.7,2.12,2.14
  Fri 20/1	10-12	Sal NB	Problems of Chapters 1,2	-	Homework nr 1 due
  Mon 23/1	10-12	Sal NB	Two-Body Problem. Orbits.	3.1-3.6
  Wed 25/1	13-15	Sal HUB	Kepler Problem. Scattering Problem.	3.7-3.12	Exercises 3.3,3.11,3.19,3.20,3.27
  Fri 27/1	10-12	Sal NB	Rigid body coordinates. Euler angles.	4.1-4.4	Exam 1.9,1.10,1.21,2.13,2.18 due
  Mon 30/1	10-12	Sal NB	Problems of Chapters 3,4,5	-	Homework nr 2 due
  Wed 1/2	13-15	Sal HUB	Euler's Theorem and rotations. Coriolis effect.	4.6-4.10	Exercises 4.1,4.2,4.3,4.5
  Fri 3/2	10-12	Sal NB	Dynamical invariants of the Rigid Body.	5.1-5.4	Exercise 5.27
  Mon 6/2	10-12	Sal NB	Euler's equations. Precession.	5.5-5.8	Exam 3.16,3.21,3.31,4.15,4.23 due
  Wed 8/2	13-15	Sal HUB	Mechanics of oscillations.	6.1-6.4	Exercises 6.11,6.12
  Fri 10/2	10-12	Sal NB	Relativistic mechanics. Covariant formulation.	7.9-7.10
  Mon 13/2	10-12	Sal NB	Problems of Chapters 6,7,8	-	Homework nr 3 due
  Wed 15/2	13-15	Sal HUB	Hamiltonian formulation. Routh's procedure.	8.1-8.3
  Fri 17/2	10-12	Sal NB	Relativistic case. Principle of least action.	8.4-8.6	Exercises 8.2,8.9,8.15,8.19
  Mon 20/2	10-12	Sal NB	Canonical transformations. Poisson Brackets.	9.1-9.5	Exam 5.6,5.26,6.4,6.13,8.1 due
  Wed 22/2	13-15	Sal HUB	Canonical equations of motion. Liouville's Theorem.	9.6,9.9
  Fri 24/2	10-12	Sal NB	Hamilton-Jacobi equation. Oscillator problem.	10.1-10.2
  Mon 5/3	10-12	Sal NB	Problems of Chapters 9,10,12	-	Homework nr 4 due
  Wed 7/3	13-15	Sal HUB	Characteristic function. Action-angle variables.	10.3-10.6	Exercise 10.14
  Fri 9/3	10-12	Sal NB	Time-dependent Perturbation Theory	12.1-12.3
  Mon 12/3	10-12	Sal NB	Time-independent Perturbation Theory. Adiabatic invariants.	12.4-12.5	Exam 9.6,9.15,10.16,12.6,12.8 due
  Wed 14/3	13-15	Sal HUB	Lagrangian and Hamiltonian formulation of continuous systems.	13.1-13.4
  Fri 16/3	10-12	Sal NB	Relativistic Fields. Noether's theorem.	13.5-13.7
  Mon 19/3	10-12	Sal NB	Finalizing the course. Finishing exercises. Discussions.
  Tue 20/3	-	-	Oral exam

• Hints and comments to some of the exercises

  These can be found in problems.pdf.

• Some comments of the students

  There exists somewhat lower level books that some people found useful:

  • Louis N. Hand, Janet D. Finch, Analytical Mechanics, Cambridge University Press 1998.
  • Stephen T. Thornton, Jerry B. Marion, Classical Dynamics of Particles and Systems, Thomson Brooks/Cole 2003 (fifth edition) (for the motion of a symmetric top)

• Lecture notes

  I will constantly post my personal lecture notes during the course. I hope these will be useful for you.

  • Lecture 1

  • Lecture 2

  • Lecture 3

  • Lecture 4

  • Lecture 5

  • Lecture 6

  • Lecture 7

  • Lecture 8

  • Lecture 9

  • Lecture 10

  • Lecture 11

  • Lecture 12

  • Lecture 13

  • Lecture 14

  • Lecture 15

  • Lecture 16

  • Lecture 17

  • Lecture 18

  • Lecture 19

  • Lecture 20

• Exam

  The examination consists of two parts. First of all, you have to do all the exercises marked as "Exam" in Table above, hand them in and be passed on those. This is necessary to be admitted for an oral examination. To be able to do that it is highly recommended to attend and to participate actively in the problem solving sessions. In addition, it is assumed that you have done and understood all the problems (marked as "Homework" in Table above) for each of the problem solving sessions. The second and crucial part is an oral exam to test understanding of theoretical foundations of classical mechanics. There is a list of typical oral exam questions.

• Responsible teacher

  Johan Bijnens, for spring 2012: Roman Pasechnik

• Contact

  Lecturer , phone 046-2223192.

  In the case of any problem, please, do not hesitate to send e-mail or give me a call.