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
Physics
A.Wolski@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 7 FHEQ First Semester 15

Aims

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


Syllabus

 

Lagrangian mechanics Lagrange’s equations derived from Newton's laws of motion

Lagrange’s equations derived from Hamilton’s principle

Examples of the application of Lagrange’s equations in mechanical systems Hamiltonian mechanics Conjugate momenta

From the Lagrangian to the Hamiltonian Derivation of Hamilton’s equations

Examples of the application of Hamilton’s equations in mechanical systems

Charged particle in an electromagnetic field

Lagrangian for a charged particle in an EM field

Hamiltonian for a charged particle in an EM field

Relativistic form of the Hamiltonian Symmetries and conservation laws

Cyclic variables Continuous symmetries and invariants;

Noether’s theorem Canonical invariants Poisson brackets Symplecticity

Liouville’s theorem Canonical transformations

Mixed-variable generating functions

The Hamilton-Jacobi equation Action-angle variables

Examples of application of canonical transformations

Continuous systems (field theory)

Derivation of field equations Symmetries, conservation laws and Noether’s theorem for fields


Teaching and Learning Strategies

Teaching Method 1 - 12 Lectures (online) of 3 hours, once per week (total 36 hours)

Teaching Method 2 - 12 Workshops (online) 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 12

        12

24
Timetable (if known)              
Private Study 126
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
on-line time controlled examination.  2 hours    60       
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
assessment 2  completed within 1 w    20       
assessment 1  completed within 1 w    20       

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.