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2010/1 Module Catalogue
 Module Code: MATM010 Module Title: HAMILTONIAN DYNAMICS
Module Provider: Mathematics Short Name: MSM.HDY
Level: M Module Co-ordinator: DERKS GL Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern
Unit(s) of Assessment
Weighting Towards Module Mark( %)
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.
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