Mathematics – A rambling mind

Understanding Einstein’s General Relativity and Curved Spacetime

Artistic drawing showing a spherical object bending a grid representing space-time with stars and galaxies surrounding it

Einstein’s later theory of General Relativity. deals with the relative acceleration of different particles under the force of gravity, including the relativistic effects of Special Relativity on these particles. In the small, it reduces to, and must be consistent with, Special Relativity, including the behaviour of light. In the large, when gravitational fields are weaker and spacetime is flat, it must reduce to and be consistent with Newton’s theory of gravity.
General Relativity more accurately describes the interactions of gravity and light.

Understanding Einstein’s Special Relativity Physics

Diagram of train at platform demonstrating relativistic time dilation and length contraction

This article provides a simple introduction to Einstein’s Special Relativity, using Prof Hermann Bondi’s k-calculus that he introduced to us in the King’s College, London Mathematics department in the late 1960s.

Analogies between Coronavirus infection modelling, telephone exchange capacity planning, Zwift game platform expansion, military simulation models and queuing theory

I reflect on my past experiences with event-based simulation, connecting it to Queuing Theory and the statistical mathematics used in telephone exchanges and modern technological applications, particularly gaming platforms like Zwift. I draw parallels between call arrival patterns and infection models, particularly regarding COVID-19. I acknowledge the influence of historical research, including work by Prof. Neil Ferguson, on understanding infection dynamics and the necessity for public health measures like social distancing. I emphasize the importance of mathematical modeling in managing infectious diseases effectively.

The Restricted Three Body Problem

This article explores the Restricted Three-Body Problem (RTBP), focusing on the dynamics of a spacecraft influenced by two larger bodies. It includes methods for analyzing motion using numerical solvers, stability investigation of Lagrange points, and the effect of varying mass ratios. Programming tasks and analyses are provided to illustrate behavior in gravitational fields over defined trajectories and conditions.

Chaos in the kitchen!

Any outcome is possible, including the kitchen sink, with highly non-linear dependence on initial conditions. For more. See http://www.ace.gatech.edu/experiments2/2413/lorenz/fall02/

Monday, Monday…

Various connotations for an alliterative Monday morning come to mind! One is that great song “Monday, Monday” by The Mamas and Papas (https://m.youtube.com/watch?v=iIo8_bMFwxs or https://m.youtube.com/watch?v=-TFddCrHlPY) I remember driving to back in the 60s, sometimes from my home in Tottenham into central London in the days when you could park free in the old Covent Garden,Continue reading “Monday, Monday…”