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 Professor A Wolski
Year CATS Level Semester CATS Value
Session 2023-24 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, including systems of particles and fields. To develop students' understanding of the fundamental relationship between symmetries and conserved quantities in physics. 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 Newton's laws of motion and Hamilton’s principle, and should be able to explain the significance of Hamilton's 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



• Lagrangian mechanics
o Lagrange’s equations derived from Hamilton’s principle
o Examples of the application of Lagrange’s equations in
mechanical systems

• Hamiltonian mechanics
o Conjugate momenta
o From the Lagrangian to the Hamiltonian
o Derivation of Hamilton’s equations
o Examples of the application of Hamilton’s equations in
mechanical systems

• Charged particle in an electromagnetic field
o Lagrangian for a charged particle in an EM field
o Hamiltonian for a charged particle in an EM field

• Relativistic motion
o Relativistic form of the Lagrangian
o Relativistic form of the Hamiltonian

• Symmetries and conservation laws
o Cyclic variables
o Continuous symmetries a nd invariants
o Noether’s theorem
o Canonical invariants
o Poisson brackets
o Symplecticity
o Liouville’s theorem

• Canonical transformations
o Mixed-variable generating functions
o The Hamilton-Jacobi equation
o Action-angle variables
o Examples of application of canonical transformations
o Canonical perturbation theory

• Continuous systems (field theory)
o Derivation of the Lagrangian field equations
o The stress-energy tensor
o Symmetries, conservation laws and Noether’s theorem for

Teaching and Learning Strategies

Teaching Method 1 - 12 Lectures (on campus) of 2 hours, once per week; plus 12 lectures (online) of 1 hours, once per week (total 36hours) .

Teaching Method 2 - 4 Problems Classes (on campus) of 2 hours, in weeks 2, 5, 8 and 11 (total 8 hours).

Teaching method 3: Online materials (videos, notes, quizzes) delivered through Canvas for students to work through in their own time.

Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours           8


Timetable (if known)              
Private Study 106


EXAM Duration Timing
% of
Penalty for late
Written examination (80%)    80       
CONTINUOUS Duration Timing
% of
Penalty for late
Coursework    20       

Recommended Texts

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