Undergraduate Course: Hamiltonian Dynamics (PHYS11012)
Course Outline
School | School of Physics and Astronomy |
College | College of Science and Engineering |
Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Availability | Available to all students |
SCQF Credits | 10 |
ECTS Credits | 5 |
Summary | This 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)
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Entry Requirements (not applicable to Visiting Students)
Pre-requisites |
It is RECOMMENDED that students have passed
Lagrangian Dynamics (PHYS10015)
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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-requisites | None |
High Demand Course? |
Yes |
Course Delivery Information
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Academic year 2024/25, Available to all students (SV1)
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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 )
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Assessment (Further Info) |
Written Exam
100 %,
Coursework
0 %,
Practical Exam
0 %
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Additional Information (Assessment) |
Degree Examination, 100% |
Feedback |
Not entered |
Exam Information |
Exam Diet |
Paper Name |
Hours & Minutes |
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Main Exam Diet S2 (April/May) | Hamiltonian Dynamics May Exam | 2:120 | | Resit Exam Diet (August) | Hamiltonian Dynamics Aug Exam | 2:120 | |
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.
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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. |
Keywords | HamDy |
Contacts
Course organiser | Dr Roger Horsley
Tel: (0131 6)50 6481
Email: rhorsley@ph.ed.ac.uk |
Course secretary | Ms Dipti Dineshwar
Tel:
Email: ddineshw@ed.ac.uk |
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