Undergraduate Course: Hamiltonian Dynamics (PHYS11012)
Course Outline
| School | School of Physics and Astronomy |
College | College of Science and Engineering |
| Course type | Standard |
Availability | Available to all students |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Credits | 10 |
| Home subject area | Undergraduate (School of Physics and Astronomy) |
Other subject area | None |
| Course website |
http://www2.ph.ed.ac.uk/~rhorsley/ |
Taught in Gaelic? | No |
| Course description | 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. |
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Tensors and Fields (PHYS10016) AND
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. |
| Additional Costs | None |
Information for Visiting Students
| Pre-requisites | None |
| Displayed in Visiting Students Prospectus? | Yes |
Course Delivery Information
| Not being delivered |
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
| None |
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)
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| Transferable skills |
Not entered |
| Reading list |
Not entered |
| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords | HamDy |
Contacts
| Course organiser | Dr Roger Horsley
Tel: (0131 6)50 6481
Email: |
Course secretary | Miss Laura Gonzalez-Rienda
Tel: (0131 6)51 7067
Email: |
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