	Department of Mathematics & Computer Science

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MA2061 Lagrangian and Hamiltonian Dynamics

MA2061(=MC256) Lagrangian and Hamiltonian Dynamics

Credits: 10

Convenor: Dr. M. D. Dampier

Semester: 2

Prerequisites:	essential: MA1001(=MC126), MA1002(=MC127), MA1051(=MC123), MA2001(=MC224)
Assessment:	Regular coursework: 20%	One and a half hour exam in May/June: 80%

Lectures:	18	Problem Classes:	5
Tutorials:	none	Private Study:	52
Labs:	none	Seminars:	none
Project:	none	Other:	none
Surgeries:	none	Total:	75

Course Description

This course is an introduction to the classical Lagrangian and Hamiltonian methods of analytical dynamics.

Aims

To introduce the powerful methods of analytical dynamics, and to apply the theory to some important physical problems. The selection of topics chosen will provide a foundation for further study, and be sufficient for the solution of most problems in dynamics that the student will encounter elsewhere in the degree.

Objectives

to understand the basic concepts of Lagrangian and Hamiltonian dynamics.
to understand how conserved quantities arise, and how to utilize them.
to use Lagrange's equations to set up and solve some significant problems.

Syllabus

Dynamics in 1-dimension, the energy diagram.
Dynamics in 3-dimensions, coordinates, constraints.
Lagrange's equations.
Symmetries and conserved quantities.
Orbits, oscillations.
Hamilton's equations, phase space.
Poisson brackets and integrals.

Transferable Skills

Most of the methods used in this module - qualitative approaches to a problem, setting up the differential equations appropriate to a physical situation, reducing the complexity of a system of differential equations by using known first integrals, and the geometric representation of problems - will be found widely applicable in other areas of applied and industrial mathematics.

Reading list

N.M.J.Woodhouse, Introduction to Analytical Dynamics, Clarendon Press, Oxford, 1987.

Details of Assessment

The final assessment of this module will consist of 20% coursework and 80% from the one and a half hour examination in May/June. The coursework contribution will come from weekly work. The examination paper will contain 4 questions with full marks obtainable for solutions to any 3.