Analytical and Computational Mechanics

About

This module aims to cover three important ideas in classical physics: Newton’s laws of motion, Newton’s law of gravitation and the wave equation.

After considering analytical solutions to each, you will look at computational solutions using the Python programming language (no background in coding is necessary; you will learn the basics on the module) and touch on ideas such as dynamical systems and chaos.

You will also examine solutions in different coordinate systems, which will give rise to familiar ideas such as Kepler’s laws of planetary motion and the inverse square law, but from a first-principles approach.

Week one
Newton’s laws of motion
Harmonic motion – SHM and damped harmonic motion
Cartesian, spherical and cylindrical coordinate systems
Forced harmonic motion and resonance

Week two
Newton’s law of gravitation
Central potentials
Rotating reference frames
Kepler’s laws

Week three
The wave equation
Deriving the 1D wave equation (longitudinal and transverse waves) and finding solutions
Waves in spherical and cylindrical systems
Wave reflection and impedance matching

Course aim

This module aims to:

- Give you, if you have studied the physical sciences, more background in classical mechanics while introducing and developing computational modelling skills.
- Increase your experience in solving and analysing problems from a variety of areas of physics through the study of analytical results.
- Increase your toolkit of methods for calculating results in different physical systems using computational methods in Python.
- Enable you to construct and defend computational results and present them in graphical format

Fee info