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
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
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
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.