Module: Classical Mechanics

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Classical Mechanics
Module Code	PHY1039 (ITS: PS223)
Faculty	Physical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

The purpose of this module is for the student to demonstrate knowledge and understanding in fundamental concepts and calculation methods of dynamics of system of particles. The Newtonian, Lagrangian and Hamiltonian formulation of mechanics will be taught. The ultimate goal the derivation (and its study) of the equations of motion for elementary mechanical systems using all the above-mentioned formulations. A secondary goal is a demonstration of mathematical methods as applied to physics.

Learning Outcomes

1. Define and understand basic concepts related to mechanical systems of particles
2. Describe and understand the three most important methodological approaches of Classical Mechanics (Newtonian, Lagrangian, Hamiltonian)
3. Apply classical dynamics methods to fundamental problems of classical mechanics (e.g. harmonic oscillators, Kepler's laws, particle collisions)
4. Understand and apply differential and integral analysis of functions (e.g. ordinary differential equations, function minimization) in physical (space-time) problems

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Core material
Tutorial	12	Tutorial problems
Independent Study	89	Material study and tutorial problems
Total Workload: 125

Section Breakdown
CRN	21284	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Lampros Nikolopoulos	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
Written Exam	In class test	20%	Week 7
Formal Examination	n/a	80%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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

Basics of functional calculus
Elements of differential and integral calculus of functions (ordinary differential equations and variational method of functions minimization)

Basic concepts
Introduction; systems of particles; mass density; centre of mass; the momentum of system of particles; angular momentum of system of particles. Newtonian dynamics (Newton's 2nd law)

Force and potential fields
Forces; kinetic and potential energy of particles; work and potential energy; conservation of energy for isolated systems.

Newton's approach
Newton's gravity and Coulomb's electric inverse square force laws, linear force law of small vibrations (harmonic oscillator)

Fundamental mechanical systems
Mass-spring system, physical pendulum, RLC electric systems as harmonic oscillators, Kepler's planar motion laws, Rutherford scattering

Langrange's approach
Lagrange equations for one-dimensional systems; the brachistochrone problem; Lagrange function of charged particles in the electromagnetic field.

Hamilton's approach
Hamilton’s principle; Hamilton’s equations of motion for simple one-dimensional systems; Poisson brackets; transition to quantum mechanics

Indicative Reading List

Books:

R. Douglas Gregory: 2006, Classical Mechanics, 1st, Cambridge University Press,

Articles:
None

Other Resources

None