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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2020/2021

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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 It is RECOMMENDED that students have passed Lagrangian Dynamics (PHYS10015)
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
High Demand Course? Yes
Course Delivery Information
Academic year 2020/21, 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 20, Summative Assessment Hours 2, Revision Session Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 52 )
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)2:00
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 secretaryMiss Helen Walker
Tel: (0131 6)50 7741
Email: hwalker7@ed.ac.uk
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