“Modern physics” in the undergraduate physics curriculum has been monopolized, on the one hand, by quantum mechanics, nuclear physics, particle physics and astrophysics. “Classical mechanics”, on the other hand, has been monopolized by Lagrangians and Hamiltonians. While these are all admittedly interesting, the topics of modern dynamics that monopolize the time and actions of most physics-degree holders, as they work in high-tech start-ups, established technology companies, or on Wall Street, are not to be found. These are the topics of nonlinear dynamics, chaos theory, complex networks, finance, evolutionary dynamics and neural networks, among others.
The links here take you to a wide range of blog posts on topics associated with the textbook “Introduction to Modern Dynamics”. Some of these posts provide the solutions to home work problems in the book.
Modern Foundations of Classical Mechanics
Top 10 Topics of Modern Dynamics
The Three-Body Problem, Longitude at Sea and Lagrange’s Points
A Wealth of Motions: Six Generations in the History of the Physics of Motion
Life in a Solar System with a Super-sized Jupiter
Spontaneous Symmetry Breaking: A Mechanical Model
Physics of the Flipping iPhone and the Fate of the Earth
Getting Armstrong, Aldrin and Collins Home from the Moon: Apollo 11 and the Three-Body Problem
Complex Dynamics
A Short History of Chaos Theory
Random Walks with Paul Langevin: Stochastic Dynamics
The Ups and Downs of the Compound Double Pendulum
Fat Fractals, Arnold Tongues and the Rings of Saturn
The Butterfly Effect versus the Divergence Meter: The Physics of Stein’s Gate
A Short History of Fractal Dimension
Edward Lorenz’ Chaotic Butterfly
Up-side-down Physics: Dynamic Equilibrium and the Inverted Pendulum
Henri Poincaré and his Homoclinic Tangle
How Number Theory Protects You from the Chaos of the Cosmos
Limit-Cycle Oscillators: The Fast and the Slow of Grandfather Clocks
Biased Double-well Potential: Bistability, Bifurcation and Hysteresis
Hermann Grassmann’s Nimble Wedge Product
The Wonderful World of Hamiltonian Maps
Applications to Complex Systems
The Physics of Robinson Crusoe’s Economy
A Random Walk in 10 Dimensions
The Physics of Modern Dynamics (with Python Programs)
The Physics of Authoritarianism: The New World Order
The Physics of U. S. Presidential Elections (why are so many elections so close?)
A Short History of Neural Networks
Locking Clocks in Strong Gravity: Synchronization in General Relativity
How to Weave a Tapestry from Hamiltonian Chaos
Special and General Relativity
The Physics of Starflight: Proxima Centauri b or Bust!
Hermann Minkowski’s Spacetime: The Theory that Einstein Overlooked
The Light in Einstein’s Elevator
Karl Schwarzschild’s Radius: How Fame Eclipsed a Physicist’s Own Legacy
The Transverse Doppler Effect and Relativistic Time Dilation
Galileo Unbound 