Module: Classical Mechanics

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Classical Mechanics
Module Code	PS223
School	School of Physical Sciences
Module Co-ordinator	Semester 1: Lampros Nikolopoulos Semester 2: Lampros Nikolopoulos Autumn: Lampros Nikolopoulos
Module Teacher	No Teacher Assigned
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Repeat examination

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

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

Lecture Series: Newtonian Dynamics I - momentum and force
Basics of kinematics in 1-2 and 3-D motion; position, velocity and acceleration. Momentum, force and Newton's 1st and 2nd laws of motion. Examples for constant (~c) linear (~x), quadratic (~x^2) and inverse square (~1/x^2) forces; free fall, charge in an constant electric field, Hooke's law, Coulomb's electrostatic force. Conservation of momentum, multiparticle systems. Conservation of momentum, Newton's 3rd law of motion.

Lecture Series: Newtonian Dynamics II - Energy
Kinetic and potential energy and Newton's laws; Work and conservation of mechanical energy; Derivation of equations-of-motion from the conservation of energy theorem; Electric and gravitational potential energy, harmonic oscillator (mass-spring and pendulum); Kinetic and potential energy of multiparticle systems, Internal potential energy of a system. Non-conservative forces and friction.

Lecture Series: Newtonian Dynamics III
Motion in 2- and 3-D space; angular momentum and angular momentum conservation law. Kinetic, potential energy and planar motion in a central force field; Coulomb's (electrostatic) Newton's (gravitational) laws; Damped and driven harmonic oscillator; physical pendulum, projectile motion, Kepler's planetary motion laws - Rutherford's scattering law

Lecture Series: Lagrangian method to 1-D systems
Lagrangian and the principle of least-action (Hamilton principle); the action integral Euler-Lagrange equations, generalized coordinates and momentum, constrained systems. Examples for free-fall/projectile motions, harmonic oscillator, pendulum problems; pulley motion Lagrangian of Multiparticle systems, the case of coupled harmonic oscillators.

Lecture Series: Hamilton's method to 1-D systems
Hamilton’s equations of motion for simple one-dimensional systems; Phase space, conservative systems and conservation of energy, the Hamiltonian of simple physical systems. Motion in phase space. Phase space diagrams. Connection with quantum mechanics.

Learning Activities:
Tutorial problems are worked out and given for homework. Physics: tutorial problems for homework with subjects relevant to the contents above. Most problems are asked to be solved using all three formulations of mechanics (Newton's, Lagrange's, Hamilton's). Maths: Cartesian and Polar coordinate systems. Vector algebra, line integral, ordinary differential equations with constant coefficients. Basic single-variable functional calculus, functions and functional minimization, Lagrange multipliers. Elements of differential and integral calculus of functions (ordinary differential equations and variational method of function minimization)

Assessment Breakdown
Continuous Assessment	40%	Examination Weight	60%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Short Answer Questions	take-home questions	20%	Every Second Week

Reassessment Requirement Type
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 1

Indicative Reading List

David Morin: 0, Introduction to Classical Mechanics, Cambridge University Press,
R. Douglas Gregory: 2006, Classical Mechanics, 1st, Cambridge University Press,
TWB Kibble and Berkshire: 0, Classical Mechanics, 5th, World Scientific Publications,
M. R. Spiegel: 0, Theoretical Mechanics; Schaum's Outline Series, McGraw-Hill,

Other Resources

None

Programme or List of Programmes

AP	BSc in Applied Physics
PAN	BSc Physics with Data Analytics
PBM	BSc Physics with Biomedical Sciences
PHA	BSc in Physics with Astronomy
SHSA	Study Abroad (Science & Health)
SHSAO	Study Abroad (Science & Health)

Archives: