Lagrangian and Hamiltonian Dynamics - MA5504

Location Term Level Credits (ECTS) Current Convenor 2017-18 2018-19
Canterbury Spring
View Timetable
5 15 (7.5) DR TC Dunning

Pre-requisites

None

Restrictions

None

2017-18

Overview

This module will present a new perspective on Newton's familiar laws of motion. First we introduce variational calculus with applications such as finding the paths of shortest distance. This will lead us to the principle of least action from which we can derive Newton's law for conservative forces. We will also learn how symmetries lead to constants of motion. We then derive Hamilton's equations and discuss their underlying structures. The formalisms we introduce in this module form the basis for all of fundamental modern physics, from electromagnetism and general relativity, to the standard model of particle physics and string theory.

Details

This module appears in:


Contact hours

40

Method of assessment

80% Examination, 20% Coursework

Preliminary reading

Douglas Gregory, "Classical Mechanics", Cambridge University Press 2006.
Herbert Goldstein, Charles P Poole; John L Safko; "Classical mechanics", Pearson/Addison Wesley, Third edition, 2002.
Patrick Hamill, "A student's guide to Lagrangians and Hamiltonians", Cambridge University Press 2014.
Emmanuele DiBenedetto, "Classical Mechanics Theory and Mathematical Modeling", Boston, MA : Birkha¨user Boston : Imprint: Birkha¨user 2011.

See the library reading list for this module (Canterbury)

See the library reading list for this module (Medway)

Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate knowledge and critical understanding of the well-established principles within Lagrangian and Hamiltonian formulations of Newtonian mechanics, particularly the dynamics of conservative systems;
2 demonstrate the capability to use a range of established techniques and a reasonable level of skill in calculation and manipulation of the material to solve problems in the following areas: variational calculus, use of generalised coordinates, application of constraints, Euler-Lagrange equations, conserved quantities, Hamiltonian formulation, the Legendre Transform, interpretation of phase portraits, use of Poisson brackets;
3 apply the concepts and principles in basic Lagrangian and Hamiltonian dynamics in well-defined contexts beyond those in which they were first studied, showing the ability to evaluate critically the appropriateness of different tools and techniques.

The intended generic learning outcomes.
On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information;
6 make use of information technology skills such as online resources (Moodle), internet communication;
7 communicate technical material competently;
8 demonstrate an increased level of skill in numeracy and computation.

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