PHY-304

Welcome to the Physical Dynamics  (PHY-304) Home Page

Course organiser: Prof Gabriele Travaglini 

Deputy course organiser: Prof Steve Thomas

Teaching assistant: Paolo Mattioli

Physical Dynamics is a more specialized and at the same time a broader study of mechanical ideas than the first year course From Newton To Einstein. The basic physics is mainly Newtonian Physics, but we will study a number of more technical ways of expressing those ideas which enable us to understand better the role of symmetry and the role of geometrical ideas in mechanics. In addition we will learn how to set up and solve in an efficient way a number of "harder'' mechanics problems.

Information about the course, homework assignments  and various resources can be accessed using the links above. This page will contain relevant news and notification of any changes to the course or this site.

Office hours: Wednesday 11-12

NEWS:  Please note that in Physical Dynamics, homeworks assignments are worth 25% of the final mark. 

Learning Outcomes

The goal of this course is to generalize the concepts of Newtonian mechanics of point particles in order to explore the relation between symmetry, geometry and conservation principles in Physics. A student who successfully completes this course will be able to:

  • state the vector Newtonian equations of motion for a system of point particles and express them in terms of total linear and angular momentum,
  • state the Newtonian conservation laws, relating them to properties of the forces acting on the particles,
  • define and use the centre of mass frame of reference, expressing linear and angular momentum of a many-particle system in terms of centre of mass variables,
  • describe simple mechanical systems in curvilinear coordinate systems by use of the Lagrangian equations of motion,
  • explain the link between symmetry and conservation laws in the Lagrangian formalism (Noether's theorem),
  • describe rotating mass distributions in terms of an angular velocity vector and a moment of inertia tensor,
  • derive the Lagrange equations of motion from a variational principle,
  • obtain the Hamiltonian description of a system starting from the Lagrangian picture,
  • describe the geometry of mechanical evolution in phase space.

You can download the programme of the 2012 course here.

Course prerequisites: PHY-116 (From Newton to Einstein) and PHY-122 (Mathematical Techniques 2) or equivalent mechanics and mathematics courses.

There are three one-hour lectures per week, and one exercise class per week. Lectures will start at five minutes past the hour and end at five minutes to the next. Punctuality is important because latecomers miss material and disturb others; latecomers may not be admitted to class. You should attend all lectures and all problem classes and hand in attempts at all exercises. Past experience shows a very clear correlation between attendence and submission of coursework, and final marks. Students whose attendance or coursework submission is inadequate without good reason will be de-registered. This can occur as early as Reading Week. Multiple de-registration will trigger termination of student status. 

 

 

There will be ten exercise sheets, which will be posted on the Web on Friday. Hand in your script by the deadline into the post box near the secretaries' offices on level 1. The homework hand in deadline is Friday at 4pm. Assignments handed in past the deadline will not be marked. You may wish to discuss the physics content of questions amongst yourselves; however copying another person's work is plagiarism and will lead to a loss of marks for both persons concerned, and possible further sanctions. 

Homework 1 (due Friday 18 January at 4)

Homework 2 (due Friday 25 January at 4)

Homework 3 (due Friday 1 February at 4)

Homework 4 (due Friday 8 February at 4)

Homework 5 (due Friday 15 February at 4)

Homework 6 (due Friday 1 March at 4)

Homework 7 (due Friday 8 March at 4)

Homework 8 (due Friday 15 March at 4)

Homework 9 (due Friday 22 March at 4)

Homework 10 (due Thursday 28 March at 4 - note unusual day)

Solutions 1 

Solutions 2

Solutions 3

Solutions 4

Solutions 5

Solutions 6

Solutions 7

Solutions 8

Solutions 9

Solutions 10

Lecture times: Wednesday 9-11 and Thursday 9-10. Excercise class: Thursday 10-11. 

 

There will be ten exercise sheets, which will be posted on the Web on Friday. Hand in your script by the deadline into the post box near the secretaries' offices on level 1. The homework hand in deadline is Friday at 4pm. Assignments handed in past the deadline will not be marked. You may wish to discuss the physics content of questions amongst yourselves; however copying another person's work is plagiarism and will lead to a loss of marks for both persons concerned, and possible further sanctions. 

The marks for this course will come from the Final Examination (75%), and from coursework (25%).

Two textbooks are:

  • Classical Mechanics, by H. Goldstein
  • Analytical Mechanics, by Louis N. Hand and Janet Finch.
For the review of Newtonian Mechanics, I mostly follow Goldstein. There are very nice lecture notes written by Prof David Tong for his course in Cambridge, covering (more or less) what we will need; you can find these here. There is also a set of lecture notes from a previous delivery of this course by Dr Bob Jones, that you can find below. An excellent, perhaps slightly more difficult textbook is This is the first book in the celebrated Course of Theoretical Physics by Landau and Lifschitz. It is a profound book, and it also contains several useful solved problems. For the study of the motion of rigid bodies, I will mostly follow this text. Furthermore, my presentation and understanding of each topic in this course is influenced by Landau and Lifshitz's. Finally, for those who are more mathematically oriented, the classic reference is I shall try to give you detailed reading references in one or more of these books to cover each topic to be discussed in Lectures.

There is also a set of lecture notes from a previous delivery of this course by Dr Bob Jones:

 

 

Please revise your notes of the course From Newton to Einstein before the course starts. It is also very important that you have good familiarity with differentiation, integration and with vector calculus.