[The University of Leicester]

Department of Mathematics



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MA2061 Lagrangian and Hamiltonian Dynamics

MA2061 Lagrangian and Hamiltonian Dynamics

Credits: 10 Convenor: Dr. M. Dampier Semester: 1 (weeks 7 to 12)
Prerequisites: essential: MA2??? desirable: MA1051
Assessment: Weekly exercises and computer practical: 40% 1.5 hour exam: 60%
Lectures: 18 Problem Classes: 5
Tutorials: none Private Study: 42
Labs: 5 Seminars: none
Project: none Other: none
Surgeries: 5 Total: 75

Subject Knowledge

Aims

This module aims to introduce the student to fundamental methods in applied mathematics, in particular the use of differential equations and their applications in dynamics. The student will also gain some experience in using the computer to solve mathematical problems.

Learning Outcomes

To know how classical mechanics produces differential equations of motion both by elementary methods and by the methods of analytical dynamics, and to be able to solve a selection of important problems in dynamics using simple qualitative methods, analytical methods, and basic numerical methods using a computer package.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, computer practical portfolio, examination.

Subject Skills

Aims

To develop students' mathematical problem solving skills, and their skills in communicating mathematical arguments, and to provide them with some basic computational skills.

Learning Outcomes

Students will have used a computer to solve some simple mathematical problems, and recorded their findings in a portfolio. Students will have improved their ability to solve problems both using pencil and paper and a computer, and will have improved their ability to write mathematical arguments.

Methods

Lectures, computer classes, problem classes.

Assessment

Marked problem sheets, marked computer practical portfolio.

Explanation of Pre-requisites

The work on differential equations and vectors which was covered in MA2??? will be needed. The module MA1051 on Introductory Newtonian Dynamics will also be useful but is not an essential prerequisite. A general mathematical knowledge from other modules is also required.

Course Description

This module will apply the new ideas on differential presented in MA2??? to important problems in classical dynamics and other areas. This is an essential module for those wishing to take certain later modules in Applied Mathematics.

Syllabus

Lagrange's equations - small oscillations. Orbits and numerical prediction. Hamiltonian systems.

Reading list

Recommended:

D. K. Arrowsmith and C. M. Place, Dynamical Systems, Chapman and Hall, 1992.

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

Resources

Problem sheets, computer rooms, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA2071 Scientific Computing Up: ModuleGuide03-04 Previous: MA2051 Fluids and Waves

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Last updated: 2004-02-21
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