A blog of Python-related topics and code.
The Kapitza pendulum is an inverted pendulum that can balance stably when driven by an oscillating vertical displacement. Its behaviour can be described using Lagrangian mechanics and modelled in Python, using the NumPy, SciPy and Matplotlib libraries.
Just a quick (20 min) analysis of the rainfall in Cambridge in February since 1996 to see how wet it has been compared with previous years. Data are taken from the amateur-maintained weather station on the roof of the Cambridge University Computer Laboratory.
An object (ship, duck, etc.) travelling across the surface of water at a constant velocity $\boldsymbol{u}$ produces a characteristic wake pattern of waves first described by Lord Kelvin. In his model of the effect, he assumed deep, still water, neglected surface tension, and restricted the …
The wave equation is a second-order linear partial differential equation describing the behaviour of mechanical waves; its two (spatial) dimensional form can be used to describe waves on a surface of water: $$ \frac{\partial^2 u}{\partial t^2} - c^2\left( \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} …
The UK Civil Aviation Authority (CAA) publishes regular statistics on the punctuality of flights arriving at and departing UK airports. These data can be retrieved with the script available on the GitHub repository accompanying this blog article: `get_data.py`.
The water–gas shift reaction is a gas-phase reaction, widely used in industry, between carbon monoxide and water to form carbon dioxide and hydrogen: This equilibrium can be analysed in terms of the Gibbs free energy of its constituents as a function of composition and temperature: …
The molar constant-pressure heat capacity, of many diatomic molecules above room temperature shows an increase from roughly to around and then higher as temperature increases. For example the graph below plots as a function of for the molecules , , , .
Simple chemical reactions can be balanced by inspection. For example, for the following reaction: since the number of each type of atom must be the same on each side of the reaction, one molecule of ethanol () must produce two molecules of and three of …
An algorithm to find the equation of the circle containing three (non-colinear) points.
A recent tweet by @iwontoffendyou posed the following problem: with reference to the figure below, what is the radius of the orange circle, which is tangent to the $y$-axis, the unit circle and the curve $y = \sqrt{x}$?
