Undergraduate Course: Symmetries of Classical Mechanics (PHYS10088)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 10 (Year 3 Undergraduate) |
Credits | 10 |
| Home subject area | Undergraduate (School of Physics and Astronomy) |
Other subject area | None |
| Course website |
None |
Taught in Gaelic? | No |
| Course description | This course provides an introduction to rotational space and space-time symmetries in classical physics. Topics covered include: vectors, bases, matrices determinants and the index notation; the general theory of Cartesian tensors; rotation and reflection symmetries; various applications including elasticity theory - stress and strain tensors; The second half of the course applies covariant and contravariant tensor analysis to special relativity. After an introduction to the physical basis of special relativity and Lorentz symmetry transformations there follows a covariant formulation of classical mechanics, force, momentum and velocity 4 vectors and particle collisions. |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | No |
Course Delivery Information
|
| Delivery period: 2011/12 Semester 1, Available to all students (SV1)
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WebCT enabled: No |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| King's Buildings | Lecture | | 1-11 | | 11:10 - 12:00 | | | | | King's Buildings | Lecture | | 1-11 | | | | | 11:10 - 12:00 | | King's Buildings | Tutorial | | 2-11 | | | | | 16:10 - 18:00 |
| First Class |
Week 1, Tuesday, 11:10 - 12:00, Zone: King's Buildings. Lecture Theatre C, JCMB |
| No Exam Information |
Summary of Intended Learning Outcomes
Upon successful completion of this course it is intended that a student will be able to:
1. be confident with the index notation and the Einstein summation convention
2. have a good working knowledge of matrices and determinants and be able to derive vector identities
3. understand the meaning and significance of rotational symmetry and its application to simple physical situations
4. be confident with the generalisation to non-orthogonal co-ordinate systems and the subsequent covariant and contravariant tensors
5. understand the foundations of special relativity and the consequences of a constant speed of light
6. have a working knowledge of relativistic particle mechanics
7. to be able to apply what has been learned in the course to solving new problems
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Assessment Information
| 100% Examination |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
- Vectors, matrices, determinants, the delta and epsilon symbols
- Rotational symmetry: transformation of bases, reflections, passive and active transformations
- Definition and transformation properties under rotations of Cartesian tensors, quotient theorem, pseudotensors, isotropic tensors
- Taylor's theorem: the one- and three-dimensional cases
- Some examples of tensors:
*conductivity tensor
*moment of inertia tensor and diagonalisation of rank-2 tensors
*continuum mechanics, the strain and stress tensors, Hooke's Law for isotropic media, fluid mechanics, the Navier--Stokes equation
- Non-orthogonal co-ordinates, covariant and contravariant tensors
- Physical basis of Special Relativity, inertial systems, constancy of the speed of light, Einstein's postulates, Lorentz transformations, time dilation, Minkowski diagrams, Doppler effect
- Covariant formulation of classical mechanics, force, momentum and velocity 4 vectors, particle collisions
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| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | SCM |
Contacts
| Course organiser | Dr Roger Horsley
Tel: (0131 6)50 6481
Email: rhorsley@ph.ed.ac.uk |
Course secretary | Miss Laura Gonzalez-Rienda
Tel: (0131 6)51 7067
Email: l.gonzalez@ed.ac.uk |
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© Copyright 2011 The University of Edinburgh - 16 January 2012 6:41 am
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