Registry
Module Specifications
Archived Version 2014 - 2015
| |||||||||||||||||||||||||||||||||||||
|
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 also see the Lagrangian and Hamiltonian approaches to classical mechanics, providing a platform for the further study of mathematical physics. | |||||||||||||||||||||||||||||||||||||
|
Learning Outcomes 1. Revise 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 | |||||||||||||||||||||||||||||||||||||
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 Revision of Ordinary Differential EquationsFirst order separable and linear differential equations; homogeneous second order linear equations with constant coefficients; solving inhomogeneous second order linear equations by method of undetermined coefficientsReview of VectorsScalar and vector products; lines and planesKinematicsVelocity, acceleration and angular velocity in Cartesian and polar coordinatesMechanics of single particleforces; principle of linear momentum for free particle; examples involving projectiles, linear oscillators and resonance, simple pendulum; work, power, conservative forces and energy; examplesCentral forcesCentral forces; Kepler s laws; application to motion of planets, comets and satellitesMechanics of finite systemsBalance of linear and angular momentum for finite systems of particles; centre of mass, reactions, two-body problemRotating framesRotating frames; velocity and acceleration relative to rotating frames; Coriolis effects; examplesAnalytical mechanicsGeneralised coordinates; Lagrange s equations and Lagrangians, Hamiltonians and Hamilton s equations; application to examples studied by other methods | |||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||
Indicative Reading List
| |||||||||||||||||||||||||||||||||||||
|
Other Resources None | |||||||||||||||||||||||||||||||||||||
| Programme or List of Programmes | |||||||||||||||||||||||||||||||||||||
| Archives: |
| ||||||||||||||||||||||||||||||||||||