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Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Mechanics
Module Code	MS339
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: David Reynolds Semester 2: David Reynolds Autumn: David Reynolds
Module Teacher	David Reynolds
NFQ level	8	Credit Rating	7.5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

This module is a mathematical introduction to classical mechanics. Students will learn sufficient basics (vectors and ordinary differential equations) to handle the mathematical problems which arise in the study of mechanics. The student will learn about the standard principles, laws and objects of mechanics, such as energy or linear momentum, and will use these tools to model physical problems mathematically. The application of the theory of central forces to satellite motion is emphasised. The student will experience the Newtonian, Lagrangian and Hamiltonian approaches to classical mechanics, providing a platform for the further study of mathematical physics.Lectures: Students will attend a series of lectures designed to introduce learners to the mathematical principles and techniques which underpin this module, with examples provided as motivation.Problem-solving: Weekly tutorials will take place where students will engage in problem solving exercises.Reading: Students are expected to fully use the recommended textbooks to supplement lectures.

Learning Outcomes

1. Solve elementary first order ordinary differential equations, and linear second order differential equations
2. Compute kinematical quantities such as velocity, angular velocity and centre of mass for finite systems of particles
3. Derive equations of motion from balance laws for linear and angular momentum for standard systems such as linear oscillators and pendula
4. Recognise and derive the equations of conic section in Cartesian and polar coordinates
5. Explain mathematical modelling of satellite motion, using deduction of Kepler's three laws from Newton's laws of motion and gravitational, as prototype
6. Apply Lagrange's equation to obtain equations of motion in terms of generalised coordinates, for specific mechanical system
7. Derive Lagrange's equations from balance law for linear momentum, for finite systems of particles
8. Derive Hamilton's equations from Lagrange's equations for finite systems of particles

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	36	Lectures
Tutorial	11	Examples classes
Independent learning time	141	Working on Exercises
Total Workload: 188

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Ordinary Differential Equations.
First order separable and linear differential equations; homogeneous second order linear equations with constant coefficients; solving inhomogeneous second order linear equations by method of undetermined coefficients.

Review of Vectors.
Scalar and vector products; lines and planes.

Kinematics.
Velocity, acceleration and angular velocity in Cartesian and polar coordinates.

Mechanics of single particle.
forces; principle of linear momentum for free particle; examples involving projectiles, linear oscillators and resonance, simple pendulum; work, power, conservative forces and energy; examples.

Central forces.
Central forces; Keplers laws; application to motion of planets, comets and satellites.

Mechanics of finite systems.
Balance of linear and angular momentum for finite systems of particles; centre of mass, reactions, two-body problem.

Rotating frames.
Rotating frames; velocity and acceleration relative to rotating frames; Coriolis effects; examples.

Analytical mechanics.
Generalised coordinates; Lagranges equations and Lagrangians, Hamiltonians and Hamiltons equations; application to examples studied by other methods.

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
In Class Test	Test on Ordinary Differential Equations	10%	Week 5
In Class Test	Test on Mechanics	15%	Week 10

Reassessment Requirement
Resit arrangements are explained by the following categories; 1 = A resit is available for all components of the module 2 = No resit is available for 100% continuous assessment module 3 = No resit is available for the continuous assessment component
This module is category 3

Indicative Reading List

R. D. Gregory: 2006, Classical Mechanics, Cambridge University Press, 9780521534093
M. Lunn: 1991, A First Course in Mechanics, Oxford University Press, 978-0-19-853433-4
D. Acheson: 1997, From Calculus to Chaos, Oxford University Press, 978-0-19-850077-3
J. .M. Knudsen and P.G. Hjorth: 1995, Elements of Newtonian Mechanics, SpringerVerlag,
J. R. Taylor: 2005, Classical Mechanics, University Science Books,

Other Resources

None

Array

Programme or List of Programmes

BSc in Applied Physics

APM

B.Sc. Applicable Mathematics

BSSA

Study Abroad (DCU Business School)

BSSAO

Study Abroad (DCU Business School)

ECSA