Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Classical Mechanics
Code PHYS470
Coordinator Prof A Wolski
Year CATS Level Semester CATS Value
Session 2019-20 Level 7 FHEQ First Semester 15


• To provide students with an awareness of the physical principles that can be applied to understand important features of classical (i.e. non-quantum) mechanical systems.
• To provide students with techniques that can be applied to derive and solve the equations of motion for various types of classical mechanical systems.
• To reinforce students’ knowledge of quantum mechanics, by developing and exploring the application of closely-related concepts in classical mechanics.

Learning Outcomes

(LO1) Students should know the physical principles underlying the Lagrangian and Hamiltonian formulations of classical mechanics, in particular D’Alembert’s principle and Hamilton’s principle, and should be able to explain the significance of these advanced principles in classical and modern physics.

(LO2) Students should be able to apply the Euler-Lagrange equations and Hamilton’s equations (as appropriate) to derive the equations of motion for specific dynamical systems, including complex nonlinear systems.

(LO3) Students should be able to use advanced concepts in classical mechanics to describe the connection between symmetries and conservation laws.

(LO4) Students should be able to apply advanced techniques, including conservation laws, canonical transformations, generating functions, perturbation theory etc. to describe important features of various dynamical systems (including systems of particles and fields) and to solve the equations of motion in specific cases.

(S1) Problem solving skills

(S2) Numeracy

(S3) Communication skills



1. Lagrangian Mechanics
1.1. Lagrange’s equations
1.2. Lagrange’s equations: some examples
1.3. Hamilton’s principle
1.4. Momenta, symmetries and conservation laws
2. Hamiltonian Mechanics
2.1. Hamilton’s equations
2.2. The principle of least action
2.3. Harmonic oscillators
2.4. Examples of Hamilton’s equations
3. Lagrangian Mechanics, Hamiltonian Mechanics, Electromagnetism and Special Relativity
3.1. Velocity-dependent potentials
3.2. Hamiltonian for a charged particle
3.3. An example: a charged, spinning ring
3.4. Relativistic motion
3.5. Covariant form of Lagrange’s equations
3.6. Hamilton’s equations in special relativity
4. Canonical Transformations
4.1. Canonical transformations
4.2. Mixed-variable generating functions
4.3. The symplectic condition
4.4. The Hamilton-Jacobi equation
4.5. Canonical perturbation theory
5. Symmetries and Conservation Laws
5.1. Canonical invariants
5.2. Infinitesimal canonical transformations
5.3. Symmetries and conserved quantities
5.4. Group theory
5.5. From classical to quantum mechanics
6. Continuum Systems
6.1. The Lagrangian for continuum systems
6.2. The stress-energy tensor
6.3. Field theories
6.4. Noether’s theorem
6.5. Local gauge invariance

Teaching and Learning Strategies

Teaching Method 1 - Lecture
Description: The course material will be delivered in a series of 36×1-hour lectures.
Attendance Recorded: Not yet decided
Notes: 36 x 1 hour lectures

Teaching Method 2 - Tutorial
Description: 6 x 1 hour tutorials/problem classes: during the tutorials/problem classes, students will work through set problems, with assistance (as needed) from lecturers/demonstrators.
Attendance Recorded: Not yet decided

Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 36


Timetable (if known)              
Private Study 108


EXAM Duration Timing
% of
Penalty for late
Assessment 1 There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When) :End of First Semester  3 hours    100       
CONTINUOUS Duration Timing
% of
Penalty for late

Recommended Texts

Reading lists are managed at Click here to access the reading lists for this module.