Classical Mechanics
FYTN09, 7.5 ECTS
Autumn 2017
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 (October 30th, 2017 - January 14th, 2018).
Introduction meeting
Monday October 30th 2017, 10:15, room HUB, theoretical physics (house K, Sölvegatan 14A).
Course Contents
This course gives a solid theoretical basis in classical mechanics in its Lagrangian and Hamiltonian formulation, with connections to modern physics.
For more detailed information on the course, see
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.
Supplimentary book: Douglas Cline Variational Principles in Classical Mechanics, University of Rochester, 2017 (for more info, see: http://classicalmechanics.lib.rochester.edu/)
Class-room activities and course schedule
We meet three times per week, typically, on Monday, Wednesday and Friday (10:15-12:00) in HUB room, unless noted otherwise (see the Schedule below). The course consists of approximately eighteen traditional blackboard lectures (2x45min) and four problem-solving sessions where we discuss your home-work assignments and work in groups. Upon request, additional problem-solving sessions can be arranged. During the course, there will be four written exam assignments. It is recommended to have the problems solved more or less simultaneously with studying the corresponding chapters in the course book. But it is strongly recommended to attend a corresponding lecture first.
Date Time Place Subject Goldstein's sections Assignments/self-study topics Mon 30/10 10-12 HUB Introduction. D'Alembert principle and Lagrangian. 1.1-1.5 Fri 3/11 10-12 HUB Hamilton's principle. Conservation theorems. 2.1,3,4,6,7 Wed 8/11 10-12 HUB Two-Body Problem. Orbits. 3.1-3.6 Thu 9/11 15-17 HUB Kepler Problem. Scattering Problem. 3.7-3.12 Mon 13/11 10-12 HUB Problem solving session I. Chapters 1-3 PS-I due Wed 15/11 10-12 HUB Rigid body coordinates. Euler angles. 4.1-4.4 Exam I due: 1.9, 1.10, 1.21, 2.13, 2.18, 3.16, 3.21 Mon 20/11 10-12 HUB Euler's Theorem and rotations. Coriolis effect. 4.6-4.10 Wed 22/11 10-12 HUB Dynamical invariants. Euler's equations. 5.1-5.8 Wed 22/11 13-15 HUB Extra problem solving session. Exam I discussion Fri 24/11 10-12 HUB Mechanics of oscillations. Relativistic mechanics. 6.1-6.4,7.9-7.10 Mon 27/11 10-12 HUB Problem solving session II. Chapters 4-7 PS-II due Wed 29/11 10-12 HUB Hamiltonian formulation. Routh's procedure. 8.1-8.3 Fri 1/11 18:00 Exam II due: 3.35, 4.15, 4.23, 5.21, 5.26, 6.4, 6.13 Wed 6/12 10-12 HUB Relativistic case. Principle of least action. Canonical transformations. 8.4-8.6, 9.1-9.4 Thu 7/12 10-12 HUB Poisson Brackets. Canonical equations of motion. Liouville's Theorem. 9.5-9.6,9.9 Thu 7/12 15-17 Andro Extra problem solving session. Exam II discussion. Fri 8/12 10-12 HUB Hamilton-Jacobi equation. Oscillator problem. 10.1-10.2 Mon 11/12 10-12 HUB Characteristic function. Action-angle variables. 10.3-10.6 Wed 13/12 10-12 HUB Time-dependent Perturbation Theory. 12.1-12.3 Fri 15/12 10-12 HUB Time-independent Perturbation Theory. Adiabatic invariants. 12.4-12.5 Mon 18/12 10-12 HUB Problem solving session III. Chapters 8-12 PS-III due Wed 20/12 10-12 HUB Lagrangian and Hamiltonian formulation of continuous systems. 13.1-13.4 Exam-III 8.1, 8.24, 9.6, 9.15, 10.5, 10.16, 12.6, 12.8 due Mon 8/1 10-12 HUB Relativistic Fields. Noether's theorem. 13.5-13.7 Tue 9/1 13-15 HUB Problems. Exam III discussion. Finalising the course. Fri 12/1 9-18 HUB Oral Exam. Mon 15/1 9-18 Oral Exam. Study groups and problem-solving sessions
The students are distributed into the following five self-study groups. Each group gets unique set of home-work exercises to be solved by and discussed at each of the problem-solving sessions.
Problem-solving session PS-I (Mon 13/11):
- Group I: 1.5, 2.7, 3.3
- Group II: 1.14, 2.12, 3.11
- Group III: 1.16, 2.14, 3.19
- Group IV: 1.23, 2.23, 3.20
- Group V: 1.22, 2.20, 3.31
Problem-solving session PS-II (Mon 27/11):
- Group I: 4.22, 5.19, 6.11
- Group II: 4.24, 5.16, 6.12
- Group III: 4.10, 5.27, 6.8
- Group IV: 4.21, 5.15, 6.9
- Group V: 4.25, 5.7, 6.17
Problem-solving session PS-III (Mon 18/12):
- Group I: 8.15, 9.10, 10.6
- Group II: 8.19, 9.21, 10.13
- Group III: 8.2, 9.8, 10.8
- Group IV: 9.28, 10.18, 12.3
- Group V: 9.23, 10.14, 12.10
Hints and comments to some of the exercises
These can be found in comments.pdf.
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 four 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 four 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.