Classical Mechanics
FYTN09, 7.5 ECTS
Autumn 2015
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 advanced 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 second part of the autumn semester (November 2nd, 2015 - January 14th, 2016).
Introduction meeting
Monday November 2nd 2015, 13:15-15:00, in the Andromeda (or "Andro") room (Astronomy building, ground floor, Sölvegatan 27).
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
We meet three times per week, namely, on Monday (13:15-15:00), Tuesday and Thursday (10:15-12:00) in Andromeda hall, unless noted otherwise. The course consists of approximately eighteen blackboard lectures (2x45min) and three-four problem solving sessions. Upon request, a few extra problem solving sessions can be arranged. There will be three homework (HW) and three written exam assignments during the course. 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, self-study Mon 2/11 13-15 Andro Introduction. D'Alembert principle and Lagrangian. 1.1-1.5 Sect. 1.2 Tue 3/11 11-13 Andro Hamilton's principle. Conservation theorems. 2.1,3,4,6,7 1.5, 1.14, 1.16, 1.23 Thu 5/11 10-12 Andro Two-Body Problem. Orbits. 3.1-3.6 2.7, 2.12, 2.14, 2.23 Mon 9/11 13-15 Andro Kepler Problem. Scattering Problem. 3.7-3.12 3.3, 3.11, 3.19, 3.20 Tue 10/11 10-12 Andro Rigid body coordinates. Euler angles. 4.1-4.4 Thu 12/11 10-12 Andro Problems of Chapters 1-3 - HW 1 due Mon 16/11 13-15 Andro Euler's Theorem and rotations. Coriolis effect. 4.6-4.10 Exam 1.9, 1.10, 1.21, 2.13, 2.18, 3.16, 3.21 due Tue 17/11 10-12 Andro Dynamical invariants. Euler's equations. 5.1-5.8 4.22, 4.24, 5.27 Thu 19/11 10-12 Andro Mechanics of oscillations. Relativistic mechanics. 6.1-6.4,7.9-7.10 6.11, 6.12 Mon 23/11 13-15 Andro Hamiltonian formulation. Routh's procedure. 8.1-8.3 8.2, 8.9, 8.19 Tue 24/11 10-12 Andro Relativistic case. Principle of least action. 8.4-8.6 Mon 30/11 13-15 Andro Problems of Chapters 4-8 - HW 2 due Tue 1/12 10-12 Andro Canonical transformations. Poisson Brackets. 9.1-9.5 Fri 4/12 15-17 Andro Canonical equations of motion. Liouville's Theorem. 9.6,9.9 Exam 3.31, 4.15, 4.23, 5.26, 6.4, 6.13 due Mon 7/12 13-15 Andro Hamilton-Jacobi equation. Oscillator problem. 10.1-10.2 9.21, 9.24 Tue 8/12 10-12 Andro Characteristic function. Action-angle variables. 10.3-10.6 10.5, 10.8, 10.13 Thu 10/12 10-12 Andro Time-dependent Perturbation Theory. 12.1-12.3 12.3, 12.10 Fri 11/12 16-18 HUB Extra provlem-solving session. - Mon 14/12 13-15 Andro Time-independent Perturbation Theory. Adiabatic invariants. 12.4-12.5 Tue 15/12 10-12 Andro Problems of Chapters 9,10,12. - HW 3 due Thu 17/12 10-12 Andro Lagrangian and Hamiltonian formulation of continuous systems. 13.1-13.4 Exam 8.1, 9.6, 9.15, 10.16, 12.6, 12.8 due Thu 7/1 10-12 Andro Relativistic Fields. Noether's theorem. 13.5-13.7 Tue 12/1 10-12 Andro Problems. Finalising the course. Thu 14/1 - - Oral Exam Hints and comments to some of the exercises
These can be found in comments.pdf.
Problem solving groups and homework assignments
Problem-solving session (Thu 12/11).
Problem-solving session (Mon 30/11).
Problem-solving session (Mon 14/12).
Some comments of the students
There exists somewhat lower level books that some students 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)
Exam
The examination consists of two parts -- written and oral exams. The written exam concerns solving the three sets of take-home exercises marked as "Exam" in Table above, timely handing them in by the respective deadline and being passed on those. Passing on all three sets of exercises is necessary to be admitted for the final (oral) examination. A passing level on a given set of exercises means that, at least, 70% of exercises are correctly solved. It is highly recommended to participate actively in the problem solving sessions. It is assumed that you have understood all the homework problems (marked as "HW" in Table above) for each of the problem solving sessions. The oral exam is the most crucial part and tests the understanding of theoretical foundations of classical mechanics. The final grade is derived based on your performance at the oral exam only.
There is a list of typical oral exam questions.
Course evaluations by students in the past
Responsible teacher and contacts
Lecturer , phone 046-2223192.In the case of any problem, please, do not hesitate to send e-mail or give me a call.