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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2014/2015
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DRPS : Course Catalogue : School of Physics and Astronomy : Undergraduate (School of Physics and Astronomy)

Undergraduate Course: Hamiltonian Dynamics (PHYS11012)

Course Outline
SchoolSchool of Physics and Astronomy CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis course assumes a knowledge of Lagrangian dynamics. The main topics covered are: the Hamiltonian formulation for systems with a finite number of degrees of freedom, the
symplectic structure of classical mechanics,
canonical transformations and Hamilton-Jacobi theory, action-angle variables and an introduction to continuous systems.
Course description Review of Lagrangian dynamics, generalised coordinates, symmetries and Noether's theorem

Hamilton's equations, conservative systems, phase space and Liouville's Theorem

Canonical Transformations, generating functions, Poisson brackets

Qualitative dynamics, behaviour of low dimensional autonomous systems, fixed points and limit cycles, simple preditor--prey systems

Hamilton-Jacobi equation, principal and characteristic functions, separation of variables, connection with quantum mechanics

Action-Angle variables, integrability, libration and rotation, the Kepler problem

Canonical Perturbation theory (both time independent and time dependent) adiabatic invariants, the KAM theorem (descriptive)
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Symmetries of Classical Mechanics (PHYS10088)
Co-requisites
Prohibited Combinations Other requirements At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.
Information for Visiting Students
Pre-requisitesNone
Course Delivery Information
Academic year 2014/15, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Supervised Practical/Workshop/Studio Hours 11, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 61 )
Assessment (Further Info) Written Exam 100 %, Coursework 0 %, Practical Exam 0 %
Additional Information (Assessment) Degree Examination, 100%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Hamiltonian Dynamics2:00
Learning Outcomes
Upon successful completion of this course it is intended that a student will be able to:
1)know how to derive Hamiltonians for simple mechanical systems and to appreciate the power of the variational approach for deriving the equations of motion;
2)be familiar with the concept of phase space for describing the motion of time dependent systems;
3)understand the significance of canonical transformations, in particular leading to the Hamilton-Jacobi equation and to the advantages of using action-angle variables;
4)be familiar with the behaviour of dynamical systems near fixed points;
5)appreciate the difference between integrable and non-integrable systems;
6)have a deeper insight into the (symplectic) structure of classical mechanics and its formal connection to quantum mechanics;
7)to be able to apply what has been learnt in the course to solving new problems.
Reading List
None
Additional Information
Course URL http://www2.ph.ed.ac.uk/~rhorsley/
Graduate Attributes and Skills Not entered
Additional Class Delivery Information Workshop/tutorial sessions, as arranged.
KeywordsHamDy
Contacts
Course organiserDr Roger Horsley
Tel: (0131 6)50 6481
Email: rhorsley@ph.ed.ac.uk
Course secretaryMs Rebecca Thomas
Tel: (0131 6)50 7218
Email: R.Thomas@ed.ac.uk
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