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2011/2 Provisional Module Catalogue - UNDER CONSTRUCTION & SUBJECT TO CHANGE
 Module Code: MAT3031 Module Title: LAGRANGIAN & HAMILTONIAN DYNAMICS (MMath)
Module Provider: Mathematics Short Name: MAT3031
Level: HE3 Module Co-ordinator: BARTUCCELLI M Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
 
Module Availability
Autumn Semester
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
Classical Dynamics  MAT1009
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. Understand the Theory of Hamilton-Jacobi and the Theory of Corresponding

 

Integrability. 
Module Content

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

 

Fundamental properties of Lagrangian Systems

 

 

Hamiltonian formulation of classical mechanics; symplectic geometry; canonical transformations; Hamiltonian flows and their fundamental features.

 

 

Symmetries, conservation laws and stability of  equilibria.

 

 

Applications will include planetary motion, rigid body dynamics and spinning tops.

 

 

Moreover, Because this is an MMath Module, Some Further Reading Material will be

 

Provided on the Theory of Hamilton-Jacobi and Corresponding Integrability.   
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).

 

A.      Fasano and S. Marmi, Analytical Mechanics, Oxford Graduates Texts (2006).

 
Last Updated
September 10