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2010/1 Module Catalogue
 Module Code: MAT3008 Module Title: LANGRANGIAN & HAMILTONIAN DYNAMICS
Module Provider: Mathematics Short Name: MS315
Level: HE3 Module Co-ordinator: BARTUCCELLI M Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
 
Module Availability
Autumn
Assessment Pattern

                        Unit(s) of Assessment
                        Weighting Towards Module Mark( %)
Coursework: Exercises and closed book class tests
25
Examination: Written examination (2 hours, unseen).
75

Module Overview
Prerequisites/Co-requisites

MAT1009 Classical Dynamics 
Module Aims

To develop the theory and methods of Lagrangian and  Hamiltonian Dynamics with emphasis on a analytical and geometrical approach.
Learning Outcomes

At the end of this course a student should have an understanding of the concepts of

 

 

Lagrangian and Hamiltonian systems, some geometric aspects and the role of symmetries. A student should be able to derive the Lagrangian and Hamiltonian equations of motion

 

 

of classical (typical) dynamical systems; work with symplectic transformations; identify simple symmetries and conservation laws; apply the Hamiltonian perturbation theory to problems related to celestial mechanics.
Module Content

Review of basic ideas from classical mechanics; Lagrange equations; Legendre transformations.

 

 

 

 

Hamiltonian formulation of classical mechanics; symplectic geometry; canonical transformations; Hamiltonian flows.

 

 

 

 

Symmetries, conservation laws and stability of  equilibria.

 

 

 

 

Applications will include planetary motion, analysis of nonlinear oscillations and elements of rigid body dynamics.
Methods of Teaching/Learning

Teaching is lectures, example classes and discussion sessions. Learning takes place through lectures, exercises and supervised  tutorials. Reading of selected material, and discussion of this material.
Selected Texts/Journals

Essential

 

 

 

 

Jorge V. Jose and  Eugene J. Saletan, Classical Dynamics – A Contemporary Approach, Cambridge university Press,  (1998).

 

 

 

 

 

Further Reading

 

 

 

 

H. Goldstein, Classical Mechanics, 2ne ed., Addison Wesley (1980).

 

 

 

 

Tom W. B. Kibble and Frank H. Berkshire, Classical Mechanics, 5th ed., Imperial College Press (2004).

 

 

 

 

J.E. Marsden and T.S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed., Springer Verlag (1998).
Last Updated

September 10