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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
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 11 (Year 4 Undergraduate) Credits10
Home subject areaUndergraduate (School of Physics and Astronomy) Other subject areaNone
Course website Taught in Gaelic?No
Course descriptionThis 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Symmetries of Classical Mechanics (PHYS10088)
Prohibited Combinations Other requirements At least 80 credit points accrued in courses of SCQF Level 9 or 10 drawn from Schedule Q.
Additional Costs None
Information for Visiting Students
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2014/15 Semester 2, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Web Timetable Web Timetable
Class Delivery Information Workshop/tutorial sessions, as arranged.
Course Start Date 12/01/2015
Breakdown of 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 )
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)Hamiltonian Dynamics2:00
Summary of Intended 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.
Assessment Information
Degree Examination, 100%
Special Arrangements
Additional Information
Academic description Not entered
Syllabus 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)
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
Course organiserDr Roger Horsley
Tel: (0131 6)50 6481
Course secretaryMs Dawn Hutcheon
Tel: (0131 6)50 7218
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