Blogs on Nonlinear Dynamics and Chaos Theory

## Random Walks with Paul Langevin: Stochastic Dynamics

Adding stochastic forces to deterministic chaos.

## A Random Walk in 10 Dimensions

A look at wandering about in a 10-dimensional landscape.

## The Transverse Doppler Effect and Relativistic Time dilation

The Doppler effect viewed at right angles to the motion.

## Locking Clocks in Strong Gravity

Synchronizing clocks near neutron stars and black holes.

## The Physics of Stein’s Gate

A fun look at the mathematics of the divergence meter from the Japanese animé “Stein’s Gate”.

## A Short History of Fractal Dimension

Fractal mathematics

## Edward Lorenz’ Chaotic Butterfly

The beginning of chaos theory.

## The Physics of U. S. Presidential Elections

Why are so many elections so close?)

## The Ups and Downs of the Compound Double Pendulum

Lagrangian mechanics of the double pendulum

## Up-side-down Physics:

Dynamic Equilibrium and the Inverted Pendulum

## Henri Poincaré and his Homoclinic Tangle

The beginning of chaos theory

## Looking Under the Hood of the Generalized Stokes Theorem

Stoke’s theorem is central to high-dimensional vector calculus

## George Stoke’s Law of Drag

The law of viscous drag

## Hermann Grassmann’s Nimble Wedge Product

The utility of the wedge product in multi-dimensional vector calculus

## Vladimir Arnold’s Cat Map

The Cat Map and Hamiltonian physics

## How Number Theory Protects You from the Chaos of the Cosmos

KAM theory and chaos of the solar system

## The Fast and the Slow of Grandfather Clocks

Limit-Cycle Oscillators

## George Duffing’s Equation

Nonlinear spring equation and chaos

## How to Weave a Tapestry from Hamiltonian Chaos

Periodic Hamiltonian chaos

## Biased Double-well Potential

Bistability, Bifurcation and Hysteresis

## Orbiting Photons around a Black Hole

Optical approximation of the gravitational deflection of light

## Getting Armstrong, Aldrin and Collins Home from the Moon

Apollo 11 and the Three-Body Problem

## Introduction to Modern Dynamics

Chaos, Networks, Space and Time (Oxford, 2019)

The physics of nonlinear dynamics and complex systems.