18 Jul 2014 No Comments

## Chapter 18: Of Cats and Their Most Wonderful Righting Reflex

Our second Lie Theoretic Systems Theory example is the theoretical physics of how a cat flips over to land on its feet when it falls, even though there are no torques on it and angular momentum must be conserved. General Comments and History That a falling cat can right itself as it falls so that […]

18 Jul 2014 No Comments

## Chapter 19: Generalised Space Curves, Coupled Waveguides and Quantum State Preparation

We conclude our study of elementary Lie Theoretic Systems Theory with an exposition on a class of problems to do with the generalised Frenet-Serret equations for space curves in $\mathbb{C}^N$ and other systems where the differential equations for a system’s state evolution include only the tridiagonal matrices even though the system’s state is transformed by […]

by Rod Vance in Lie Groups: What They Do, Lie Theory, Part 1: Lie Theoretical Systems Theory Tags: Berry Phase, Coupled Optical Waveguide, Frenet-Serret Equations, Frenet-Serret Frame, Nearest Neighbour Coupling, Optical Waveguide, Parallel Transport, Quantum Measurement, Quantum Mechanics, Quantum State, Quantum State Preparation, Smallest Containing Lie Algebra, Space Curve, Tridiagonal Matrix