|
| Module Availability |
| Spring |
|
|
| Assessment Pattern |
|
Unit(s) of Assessment
|
Weighting Towards Module Mark( %)
|
|
Coursework
|
40
|
|
Test
|
60
|
|
Qualifying Condition(s)
An overall aggregate mark of 50% for the module is required to pass the module.
|
|
|
|
| Module Overview |
| This module builds on the level 3 module Lagrangian and Hamiltonian Dynamics and provides a further development of geometric methods in Hamiltonian Dynamics and an extension to Hamiltonian wave equations. |
|
|
| Prerequisites/Co-requisites |
| MAT3008 Lagrangian and Hamiltonian Dynamics |
|
|
| Module Aims |
| The aim of this module is extend the geometric methods for finite dimensional Hamiltonian systems, introduced in the level 3 module Lagrangian and Hamiltonian Dynamics and to introduce students to infinite dimensional Hamiltonian systems, especially Hamiltonian wave equations. |
|
|
| Learning Outcomes |
At the end of the module a student should be able to:
• State the properties of Poisson structure and manipulate with Poisson brackets
• Identify symmetries, find conservation laws and relative equilibria
• Determine the stability or instability of equilibria and relative equilibria
• Apply to concepts above to examples like N-body dynamics, rigid bodies and spinning tops
• Determine the Poisson structure related to some Hamiltonian wave equations, identify solitary waves/fronts and their relation to relative equilibria and analyse their stability in simple examples. |
|
|
| Module Content |
This module contains the following topics:
• Revision of key concepts of the level 3 module on Lagrangian and Hamiltonian Dynamics
• Symplectic forms, Poisson brackets and Poisson structures
• Symmetries, conservation laws and relative equilibria
• Stability of equilibria and relative equilibria
• Selected topics from: N-body dynamics, rigid body dynamics and spinning tops
• Introduction to Hamiltonian wave equations, (travelling) solitary waves/front and stability |
|
|
| Methods of Teaching/Learning |
Teaching is by lectures, tutorials and example classes. Learning takes place through lectures, exercises (example sheets), preparation for tests and background reading.
There will be 3 contact hours for 10 weeks consisting of lectures, tutorials and example classes.
|
|
|
| Selected Texts/Journals |
• J.V. José and E.J. Saletan.
Classical Dynamics: A Contemporary Approach.
Cambridge University Press (1998).
• H. Goldstein.
Classical Mechanics, 2nd ed.
Addison Wesley (1980).
• J.E. Marsden and T.S. Ratiu.
Introduction to Mechanics and Symmetry, 2nd ed.
Springer Verlag (1998).
• F. Scheck.
Mechanics: From Newton's Laws to Deterministic Chaos.
Springer Verlag (1990).
• L.D. Faddeev and L.A. Takhtajan.
Hamiltonian Methods in the Theory of Solitons
Springer Verlag (1987). |
|
|
| Last Updated |
| 29 October 2009 |
|
