# LAGRANGIAN & HAMILTONIAN DYNAMICS - 2018/9

Module code: MAT3008

Module Overview

This module introduces some fundamental concepts in analytical dynamics and illustrates their applications to relevant problems. The module covers the calculus of variations, Lagrangian and Hamiltonian formulations of dynamics, Poisson brackets, canonical transformations and Hamilton-Jacobi equations.

The module leads, among other things, to a deeper understanding of the role of symmetries  and conservation laws. This course lays the foundations for the Year 3 module  Quantum Mechanics  (MAT3039).

Module provider

Mathematics

BARTUCCELLI Michele (Maths)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 6

JACs code: G121

Module cap (Maximum number of students): N/A

Module Availability

Semester 2

Prerequisites / Co-requisites

Classical Dynamics  MAT1036

Module content

Indicative content includes:

• Generalised coordinates, calculus of variations, Lagrangian and Euler-Lagrange equations.

• Planetary motion.

• Legendre transform, Hamiltonian and canonical equations of motion.

• Hamilton-Jacobi method.

Assessment pattern

Assessment type Unit of assessment Weighting
Examination EXAMINATION 80
School-timetabled exam/test IN-SEMESTER TEST (50 MINS) 20

Alternative Assessment

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:

·         Ability to choose  appropriate  generalised coordinates to describe a system

·         Ability to identify simple symmetries and conservation laws.

·         Subject knowledge through the recall of key definitions, theorems and their proofs.

·         Analytical ability through the solution of unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

·         One two hour examination  at the end of Semester 1; worth 80% module mark.

·         One in-semester test; worth 20% module mark.

Formative assessment and feedback

Students receive written feedback via a number of marked coursework assignments over an 11 week period.

Module aims

• Introduce students to the Lagrangian and Hamiltonian formulations of dynamics
• Enable students to understand the role of  symmetries and conservation  laws
• Illustrate the application of various techniques for solving frequently encountered problems in analytical dynamics

Learning outcomes

Attributes Developed
1 Choose an appropriate set of generalised coordinates to describe a system CT
2 Apply the Lagrangian and Hamiltonian formulations of dynamics to determine the evolution of a system KCT
3 Use the Hamilton-Jacobi method to solve separable systems KC

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Independent Study Hours: 117

Lecture Hours: 33

Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• Introduction to generalised coordinates, functionals, Lagrangian and Hamiltonian, principle of least action.

• Experience (through demonstration) of the methods used to determine the dynamics of a system by means of the Lagrangian and Hamiltonian formulation of dynamics.

The learning and teaching methods include:

• 3 x 1 hour lectures per week x 11 weeks. Blackboard lectures.  Q + A opportunities for students.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.