This course covers analytical mechanics, the final level of classical mechanics for undergraduates. The Big Three core topics for this course are Rigid Body Motion, Normal Modes for Coupled Oscillations and Lagrangian and Hamiltonian Mechanics. To these I will add other topics, like fluid mechanics and classical fields (and possibly chaotic motion, time permitting).
Students are assumed to have had an exposure to classical mechanics beyond the first-year level, such as seen in Physics 2E03. I will make an effort to keep the discussion self-contained by briefly viewing the needed background material.
Although I usually work from my own notes, for this subject these are a work in progress. There are a variety of good textbooks on classical mechanics, and I will list the ones here that I think will be the most useful. In past years the textbook for this course has been Classical Mechanics by Taylor. See below for procedural course information. The table of contents of the notes provides the most detailed syllabus, but the main items are also paraphrased here.
SYLLABUS
- Rigid Body Motion
- Review of Vector Mechanics
- When is rigid body motion relevant?
- Non-inertial reference frames
- Coupled Oscillators
- General theory of small oscillations
- Normal Modes
- Continuum limit and fields
- Electromagnetic fields
- Fluids
- Continuum mechanics
- Perfect fluids
- Newtonian fluids
- Rotating fluids
- Canonical Methods
- Lagrangian mechanics
- Principle of least action
- Hamiltonian methods
- Canonical transformations
- Chaos
- Sensitivity to initial conditions
- Chaotic motion
COURSE INFORMATION
The procedural information relevant to this course is given below.
Lectures
Classes are in person in the Winter 2026 term and will be held from 1:30 – 2:20 on Monday, Wednesday and Thursday of each week of the term. The room location will be shown on Mosaic
For best results you should pre-read sections of the lecture notes and/or the textbook before coming to class.
Attendance to the lectures is certainly not compulsory, but if you come I do ask you to pay attention and not disrupt the class with personal conversation or social media. I will do what I can to ensure that you do not have to gnaw your own arm off to stay awake.
Textbook
Watch this space for textbook recommendations.
For those seeking alternative viewpoints, alternative presentations can be found in the following books:
Office Hours
Because I spend half my time at Perimeter Institute I may be hard to find in my office. So it is worth setting up any appointments in advance, and the best way to do so is to contact me by email at cburges – at – mcmaster.ca (notice the single “s” – sigh). I will also linger immediately after the scheduled lecture times since we are already together then. Otherwise, feel free to arrange another time with me on an individual basis. (I will make a point of being there for scheduled appointments, so if you do set up an appointment, please show up or give me adequate warning that you cannot make it!)
TA
Recent cutbacks mean there might not be a TA for this course if the enrolment is less than 25 (which it usually is). If so then the course will become more descriptive with a reduced emphasis on assignments.
Assignments
The course work involves completing several assignments (whose amount and length depends on TA availability). Like any worthwhile subject, Classical Mechanics is a contact sport and so is only really learned by doing. It is very very strongly recommended to work the assignments even if you only audit the course.
The scheduling of assignments will be agreed in the first lecture.
Assignment 1:
Assignment 2:
Assignment 3:
There will not be assignments in the week of Feb. 23 to Feb 27 due to the midterm.
You are welcome to work together on figuring out the assignments, though everyone must write up and submit their own solutions. It should go without saying, while you are allowed (for assignments) to consult internet material about conceptual information, you are never permitted to plagiarize material from the internet (or to use internet cheating tools like chegg) when preparing any work for marks, including assignments.
Midterm Exam
Since the course is online, the midterm test will be held in class on Thursday February 26nd, 2026.
The midterm provides the best possible practice for the final exam, so it would be silly not to write it. Those who do not write the midterm for whatever reason can avail themselves of marking Option B below.
Perhaps needless to say, you are never permitted to plagiarize material from the internet when performing a midterm exam.
Final Exam
The Final Exam will be held during the April examination session, and will likely be an oral exam (and will include your essay as a topic of questions).
You are never permitted to plagiarize material from the internet when preparing any marked work, and this is especially true for final exams.
Marking Scheme
The course marks are completely based on the weekly assignments, the mini-quizzes, the midterm test, the term project and the final exam. The term mark will be computed from these according to whichever of the following formulae maximizes your final mark:
- A) Ass.: 20% Midterm: 40% Final Exam: 40%
- B) Ass.: 20% Midterm: 0% Final Exam: 80%
- C) Ass.: 10% Midterm: 40% Final Exam: 50%
- D) Ass.: 10% Midterm: 0% Final Exam: 90%
You do not have to choose in advance which one you want; I will compute all four and give you whichever is the highest.
Part of the reason for providing you this menu of alternatives is to allow you to accommodate the imponderables of your own life, such as unexpected illnesses and the like. The purpose of doing so is to make this flexibility open to everybody in the class, and not just to those who wish to make special arrangements with me, or with the Associate Dean. In particular, this my preferred way to deal with MSAF applications in this class.
Additional Work and Supplemental Exam:
Additional work will NOT be available for students who might wish to improve their marks. The standard McMaster rules apply regarding the availability of supplemental exams.
Reading you your rights:
The Centre for Student Development offers free academic skill support.
Although hopefully it does not need saying, be warned that the University does not tolerate cheating, plagiarism and the like:
THE UNIVERSITY VALUES ACADEMIC INTEGRITY. THEREFORE ALL STUDENTS MUST UNDERSTAND THE MEANING AND CONSEQUENCES OF CHEATING, PLAGIARISM AND OTHER ACADEMIC OFFENCES UNDER THE CODE OF STUDENT CONDUCT AND DISCIPLINARY PROCEDURES
(see http://www.mcmaster.ca/academicintegrity for more information).