Undergraduate Course: Symmetries of Classical Mechanics (PHYS10088)
Course Outline
School  School of Physics and Astronomy 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Year 3 Undergraduate) 
Availability  Available to all students 
SCQF Credits  10 
ECTS Credits  5 
Summary  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. 
Course description 
 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.

Information for Visiting Students
Prerequisites  None 
Course Delivery Information
Not being delivered 
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

Additional Information
Graduate Attributes and Skills 
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 

