Advanced Mechanics (PHYS*3400)

Code and section: PHYS*3400*01

Term: Fall 2021

Instructor: Eric Poisson


General information

Calendar description

This course covers Lagrangian mechanics and Hamiltonian mechanics. Topics include least action principles, Poisson brackets, Liouville's theorem, Hamilton- Jacobi theory, the transition to quantum mechanics and introduction to non-linear dynamics.

Class schedule and location

Tuesday and Thursday, 10:00am to 11:20am, MacKinnon (MCKN) 309.


There are no tutorials for this course.

Midterm exam

Tuesday October 19, 10:00am, in class.

Final examination

Thursday December 16, 2:30pm, room TBA. 

Final exam weighting

40% (Scheme A) or 45% (Scheme B); see below.

Course website

On Courselink.

Instructor information


Eric Poisson (
Office location and phone number
MacNaughton 452, 519-824-4120 x53653

Office hours

Office hours are on Tuesday afternoons, from 1:30pm to 4:30pm. I am generally available outside of these times. Please schedule an appointment if you have trouble finding me.
I am very much an informal guy, and I prefer to be addressed simply as “Eric”. I don’t particularly like being subjected to such pompous titles as Doctor, Professor, or Your Grace. My field of research is general relativity, including black holes and gravitational waves. For additional details, please consult my profile.

Graduate Teaching Assistant information

There is no TA for this course.

Course content


This course covers advanced techniques of classical mechanics, focusing mostly on the Lagrangian and Hamiltonian formulations of the laws of mechanics. It begins with a review of the usual Newtonian formulation and ends with a few lectures on frontier aspects.


The formal prerequisites for this course are PHYS*2310 (Mechanics) and MATH*2270 (Applied Differential Equations). You are expected to thoroughly master the material covered in these courses. You are also expected to master other areas of mathematics as well, such as curvilinear coordinates, Taylor expansions, total and partial differentiation, integration, trigonometric functions, etc.      


This is a demanding course in which you will learn sophisticated methods of theoretical physics. These are useful well beyond the context of this course; Lagrangian methods apply, for example, to field theories such as electromagnetism, the standard model of particle physics, and general relativity. This is physics for
grown-ups, and it is imperative that you conduct yourself as a grown-up while taking this course.
This means, most of all, taking responsibility for your own education. In practice, this means that you will spend a considerable amount of time outside of class hours teaching yourself the material.    

The mastery of physics does not come easily to anyone. You must work hard at it, and the work must be done by you, and no one else. My role as your instructor is to help you in this process. I do not believe, however, that I can truly teach you the material. I can lecture on it, give you an orientation, and illustrate the basic ideas, but all this will not make you learn the material. (This may only give you a false impression that you have learned it.) What you must do instead is teach yourself, and my role as your instructor is mostly to help you teach yourself. Knowledge and understanding will come from your own efforts; they cannot be directly transmitted from me to you. It is imperative that you come prepared to do your own learning in this course, and be willing the spend the time that this requires.    

My lectures will be given at a level that is slightly lower than the coverage in the lecture notes. My purpose in the lectures is to introduce the main themes and talk about them in fairly general terms. But attending the lectures will not be enough; you will be expected to master the material at the higher level set in the lecture notes. It will be your job to go through the lecture notes in detail, outside of class hours, following the schedule that I set in class. You are expected to read the text carefully, go through all the mathematical steps, fill the gaps, and work through the exercises that are scattered throughout the notes. Doing all this will prepare you very well to do the problems at the end of each chapter, and solving these problems will prepare you very well for the midterm and final exams.   

If you follow this course of action you will do very well in this course. And if you follow this advice in other courses as well, your education in physics will be rock-solid. If, however, you fail to read the notes, go through the math, do the exercises and problems, or if you rely too much on others to find answers for you, then you will acquire no useful skills from this course. And if this is your general attitude in other courses as well, your education in physics will turn out to be useless. Physics is challenging. Live up to the challenge!


There are no labs for this course.


There are no tutorials for this course. 

Lecture, tutorial, and assignment schedule

The following table provides a very rough guide of the material covered during each week of the semester, as well as key information regarding deadlines. All dates are tentative; check Courselink regularly to get the most updated information. Regular attendance at lectures is the best way to ensure that you are up to date on the relevant course material.

Week Material Activity
0: Sept 9 Newton’s law;  inertial frames  
1: Sept 14, 16 Mechanics of a single body    
2: Sept 21, 23 Mechanics of a system of bodies Assignment 1
3: Sept 28, 30 Kepler’s problem  
4: Oct 5, 7 Lagrangian mechanics: formulation   
5: Oct 14 Lagrangian mechanics: applications Assignment 2
6: Oct 19, 21 Lagrangian mechanics: applications Midterm exam
7: Oct 26, 28 Lagrangian mechanics: applications  
8: Nov 2, 4 Hamiltonian mechanics: formulation  
9: Nov 9, 11  Hamiltonian mechanics: applications  Assignment 3
10: Nov 16, 18 Frontiers  
11: Nov 23, 25 Frontiers  
12: Nov 30, Dec 2 Frontiers  Term project

Course evaluation

Marking schemes

The final mark for the course will be the highest of the two marks calculated under the following schemes A and B. No other marking schemes will be considered.

Scheme Assignments Term Project Midterm Final
A 15 10 35 40
B 15 10 30 45

A set of three homework assignments will also be made available on Courselink, to be returned before the assigned due date. A penalty of 20% per day will be applied to any late assignment, and no assignment will be accepted after it has been marked. Special arrangements for late submission without penalty require a good reason and must be made well ahead of time.

The term project is a long assignment in which you are asked to describe the motion of a satellite around a black hole. It is attached at the end of the lecture notes. The term project must be completed before the last week of classes. It is imperative that you get started early in order to have any hope of completing it in time.  The term project includes a computational component, for which you will be entirely responsible. 

The midterm and final exams are closed-book exams, meaning that you will not be allowed to consult your notes nor any other source of information. You will, however, be provided with a formula sheet. Calculators may be required; only non-programmable pocket calculators are permitted. Personal communication or entertainment devices are not permitted during the exams.

(Not) Working with other students

All work submitted for grading in this course must be each individual student’s own work. While students are encouraged to share thoughts and ideas prior to writing up solutions to homework assignments, it is not acceptable to share assignment solutions. The assignments are not group projects, and it is important that you do not show your final written solutions to other students.

Completing assignments is an essential part of your preparation toward midterm and final exams. A serious attempt to do the work yourself, independently of others, will provide you with a very good preparation. Relying too much on others to provide pieces of solutions will give you a very poor preparation.

Getting help

Please consult with Eric whenever the need arises. Do not wait too long before getting the help you need; it may be too late by then.

Course resources

Required text

There is no required text for this course. Detailed lecture notes are available on CourseLink and on the departmental website.

Recommended texts

You may find it useful to consult the following references: 

  • David Morin, Introduction to Classical Mechanics (1st Edition, Cambridge University Press, 2008; QA805 .M822)
  • Herbert Goldstein, Charles P. Poole, and John L. Safko, Classical Mechanics (3rd Edition, Addison Wesley, 2002; QA 805.G6) 
  • Stephen T. Thornton and Jerry B. Marion, Classical Dynamics of Particles and Systems (5th Edition, Brooks Cole, 2003; QA 845.M38)

The book by Morin is at a slightly lower level than this course, but it is very good and contains a large selection of problems. The book by Goldstein, Poole, and Safko is the bible of classical mechanics, and is at a slightly higher level than this course. The book by Thornton and Marion is another standard, also at a slightly higher level. 

Course policies

Grading policies

See Course Evaluation (Marking schemes), above. 

Course policy on group work

See Course Evaluation ((Not) working with other students), above. 

Course policy on electronic devices and recording of lectures

What you do with your laptop, smart phone, tablet, etc, during lectures is your own business, so long as it does not create a distraction for your classmates or the instructor. (The instructor is easily distracted.) If such a distraction arises you will be asked to leave the classroom.

Electronic recording of classes is expressly forbidden without consent of the instructor. When recordings are permitted they are solely for the use of the authorized student and may not be reproduced, or transmitted to others, without the express written consent of the instructor. 

University Policies

Academic Consideration

When you find yourself unable to meet an in-course requirement because of illness or compassionate reasons, please advise the course instructor in writing, with your name, id#, and e-mail contact. See the Undergraduate Calendar for information on regulations and procedures for academic consideration.

Academic Misconduct

The University of Guelph is committed to upholding the highest standards of academic integrity and it is the responsibility of all members of the University community, faculty, staff, and students to be aware of what constitutes academic misconduct and to do as much as possible to prevent academic offences from occurring.

University of Guelph students have the responsibility of abiding by the University’s policy on academic misconduct regardless of their location of study; faculty, staff  and students have the responsibility of supporting an environment that discourages misconduct. Students need to remain aware that instructors have access to and the right to use electronic and other means of detection. Please note: Whether or not a student intended to commit academic misconduct is not relevant for a finding of guilt. Hurried or careless submission of assignments does not excuse students from responsibility for verifying the academic integrity of their work before submitting it. Students who are in any doubt as to whether an action on their part could be construed as an academic offence should consult with a faculty member or faculty advisor.

The Academic Misconduct Policy is detailed in the Undergraduate Calendar.


The University of Guelph is committed to creating a barrier-free environment. Providing services for students is a shared responsibility among students, faculty and administrators. This relationship is based on respect of individual rights, the dignity of the individual and the University community’s shared commitment to an open and supportive learning environment. Students requiring service or accommodation, whether due to an identified, ongoing disability or a short-term disability should contact Student Accessibility Services (SAS) as soon as possible.

For more information, contact SAS at 519-824-4120 ext. 56208.

Course Evaluation

The Department of Physics requires student assessment of all courses taught by the Department. These assessments provide essential feedback to faculty on their teaching by identifying both strengths and areas of improvement. In addition, student assessments provide part of the information used by the Department Tenure and Promotion Committee in evaluating the faculty member’s contributions in the area of teaching. You are therefore encouraged to take the evaluation procedures seriously, and to provide feedback about this course and its instructor.

Drop date

The last date to drop one-semester courses, without academic penalty, is 3 December 2021. For regulations and procedures for Dropping Courses, see the Undergraduate Calendar.