Module Specifications..
Current Academic Year 2023  2024
Please note that this information is subject to change.
 
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 abovementioned 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 (spacetime) problems  
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 12 and 3D 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 equationsofmotion from the conservation of energy theorem; Electric and gravitational potential energy, harmonic oscillator (massspring and pendulum); Kinetic and potential energy of multiparticle systems, Internal potential energy of a system. Nonconservative forces and friction. Lecture Series: Newtonian Dynamics III Motion in 2 and 3D 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 1D systems Lagrangian and the principle of leastaction (Hamilton principle); the action integral EulerLagrange equations, generalized coordinates and momentum, constrained systems. Examples for freefall/projectile motions, harmonic oscillator, pendulum problems; pulley motion Lagrangian of Multiparticle systems, the case of coupled harmonic oscillators. Lecture Series: Hamilton's method to 1D systems Hamilton’s equations of motion for simple onedimensional 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 singlevariable 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)  
 
Indicative Reading List
 
Other Resources None  
Programme or List of Programmes  
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