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MA1051 Newtonian Dynamics

MA1051 Newtonian Dynamics

Credits: 10 Convenor: Dr. M. Dampier Semester: 2 (weeks 15 to 26)
Prerequisites: essential: MA1001, MA1002
Assessment: Weekly exercises: 20% one and a half hour exam: 80%
Lectures: 20 Problem Classes: 4
Tutorials: none Private Study: 46
Labs: none Seminars: none
Project: none Other: none
Surgeries: 5 Total: 75

Subject Knowledge

Aims

This module aims to introduce the student to basic ideas in Newtonian Dynamics, using vector methods where appropriate, but also linking the treatment with ideas from elementary differential equations. Collisions, motion under gravity, one-dimensional oscillations, and Keplerian orbits constitute the main topics covered.

Learning Outcomes

To know how classical mechanics conceptualises problems. To be able to write down equations of motion and initial conditions for some representative problems, and to use elementary mathematical techniques to solve problems and to interpret the solutions.

Methods

Lectures, optional surgeries, problem classes.

Assessment

Marked problem sheets, examination.

Subject Skills

Aims

To introduce skills of modelling physical systems, to develop students' mathematical problem solving skills, and their skills in communicating mathematical arguments.

Learning Outcomes

Students will have improved their ability to solve problems using pencil and paper, and will have improved their ability to write mathematical arguments.

Methods

Lectures, problem classes.

Assessment

Marked problem sheets.

Explanation of Pre-requisites

The work on differential equations and vectors which was covered in MA1002 will be consolidated and extended by this module. Material from MA1001 on curves will also be built upon. Previous knowledge of applied mathematics although desirable is not essential.

Course Description

This module covers the basic concepts of classical mechanics and is an essential module for those wishing to take certain later modules in Applied Mathematics, for example Fluids and Waves.

Syllabus

Introduction - motion, velocity, speed. Newton's first law. Conservation of momentum - mass, kinetic energy, coefficient of restitution. Motion under gravity - acceleration, force, Newton's second law. Galileo's law - potential energy, smooth constraints. Motion in 1-dimension - potential, energy conservation. The energy diagram - periodic motion. Equilibrium - small oscillations. Orbital motion - Newton's law of gravitation, escape velocity. Circular orbits - 2-body problem. The conservation laws - Keplerian motion.

Reading list

Recommended:

P. Dyke and R. Whitworth, Guide2 Mechanics, Palgrave, 2001.

Resources

Problem sheets, lecture rooms.

Module Evaluation

Module questionnaires, module review, year review.

Next: MA1061 Probability Up: ModuleGuide03-04 Previous: MA1011 Methods of Applied Mathematics I

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Last updated: 2004-02-21
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