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 spacetime 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 latter part 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 the covariant formulation of classical mechanics and electromagnetism including: force, momentum and velocity 4 vectors, the Maxwell tensor and particle collisions. 
Information for Visiting Students
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information

Delivery period: 2014/15 Semester 2, Available to all students (SV1)

Learn enabled: Yes 
Quota: None 

Web Timetable 
Web Timetable 
Course Start Date 
12/01/2015 
Breakdown of Learning and Teaching activities (Further Info) 
Total Hours:
100
(
Lecture Hours 37,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
61 )

Additional Notes 

Breakdown of Assessment Methods (Further Info) 
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %

Exam Information 
Exam Diet 
Paper Name 
Hours & Minutes 

Main Exam Diet S2 (April/May)   2:00  
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 nonorthogonal coordinate 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. understand the implications for electromagnetism.
8. to be able to apply what has been learned in the course to solving new problems

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 threedimensional cases
 Some examples of tensors:
*conductivity tensor
*moment of inertia tensor and diagonalisation of rank2 tensors
*continuum mechanics, the strain and stress tensors, Hooke's Law for isotropic media, fluid mechanics, the NavierStokes equation
 Nonorthogonal coordinates, 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 and electomagnetism, force, momentum and velocity 4 vectors, particle dynamics and collisions, Maxwell tensor, Lorentz transformations of electric and magnetic fields.

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  Mrs Bonnie Macmillan
Tel: (0131 6)50 5905
Email: Bonnie.MacMillan@ed.ac.uk 

