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 Physics A.Wolski@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2020-21 | Level 7 FHEQ | First Semester | 15 |
Aims |
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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 |
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(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. |
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(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. |
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(LO3) Students should be able to use advanced concepts in classical mechanics to describe the connection between symmetries and conservation laws. |
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(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. |
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(S1) Problem solving skills |
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(S2) Numeracy |
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(S3) Communication skills |
Syllabus |
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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 |
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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 |
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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 |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |