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 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
Prerequisites  None 
Displayed in Visiting Students Prospectus?  No 
Course Delivery Information

Delivery period: 2011/12 Semester 1, Available to all students (SV1)

WebCT enabled: No 
Quota: None 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
King's Buildings  Lecture   111   11:10  12:00     King's Buildings  Lecture   111      11:10  12:00  King's Buildings  Tutorial   211      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 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. 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, force, momentum and velocity 4 vectors, particle collisions

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 GonzalezRienda
Tel: (0131 6)51 7067
Email: l.gonzalez@ed.ac.uk 

