Instabilities and Catastrophes

Chapter1 : Introduction to Buckling

• 1.1 Experiment on an Arch
• 1.2 Collapse of the Arch

Chapter2 : Stability and Instability

• 2.1 Equilibrium
• 2.2 Stable or Unstable?
• 2.3 Idea of a Load

Chapter3 : The Fold Catastrophe

• 3.1 Instability at a Fold
• 3.2 Explosion of a Star
• 3.3 Jump towards a Black-Hole

Chapter4 : Symmetry-Breaking

• 4.1 Leonhard Euler
• 4.2 Buckling of a Column
• 4.3 Pitchfork Bifurcations
• 4.4 Dangerous Pitchfork

Chapter5 : Floating Logs

• 5.1 Challenge Question
• 5.2 The Correct Answer
• 5.3 Pitchfork in the Log
• 5.4 Ship Stability adn Capsize

Chapter6 : Writhing of DNA

• 6.1 DNA Molecule
• 6.2 Super-coiling of DNA
• 6.3 Experiments on Rods

Chapter7 : Catastrophe Theory

• 7.1 Typical Events
• 7.2 Catastrophe Theory
• 7.3 Idea of two controls
• 7.4 Angry Dogs
• 7.5 Sudden Attack
• 7.6 Catastrophe Machine

Chapter8 : Multi-Mode Concepts

• 8.1 Energy Landscapes
• 8.2 Two-D Landscapes
• 8.3 Towards Infinity
• 8.4 Engineers need Mathematics
• 8.5 Evolution of a spinning Planet

Chapter9 : Oscillatory Instabilities

• 9.1 The Tacoma Narrows Disaster
• 9.2 Galloping
• 9.3 Two Examples of Galloping
• 9.4 The Wobbly Millennium Bridge

Chapter10 : Stability of Motion

• 10.1 Extensible Pendulum
• 10.2 Fluid Turbulence
• 10.3 Mysterious Stabilization

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