Utility Of Quaternions In Physics

<p>Introduction</p><p>General remarks on the place of Quaternions in Physics </p><p>Cartesian form of some of the results to follow </p><p>Definitions </p><p>Properties of ζ </p><p>Fundamental Property of D </p><p>Theorems in Integration </p><p>Potentials </p><p>Brief recapitulation of previous work in this branch </p><p>Strain Stress-force Stress-couple </p><p>Stress in terms of strain </p><p>The equations of equilibrium </p><p>Variation of temperature</p><p>Small strains </p><p>Isotropic Bodies </p><p>Particular integral of the equation of equilibrium </p><p>Orthogonal coordinates</p><p>Saint-Venant's torsion problem</p><p>Wires</p><p>Electrostatics-general problem</p><p>The force in particular cases </p><p>Nature of the stress </p><p>Magnetism-magnetic potential force induction</p><p>Magnetic solenoids and shells </p><p>Electro-magnetism-general theory </p><p>Electro-magnetic stress </p><p>Preliminary</p><p>Notation </p><p>Euler's equations </p><p>The Lagrangian equations</p><p>Cauchy's integrals of these equations </p><p>Flow circulation vortex-motion </p><p>Irrotational Motion </p><p>Motion of a solid through a liquid </p><p>The velocity in terms of the convergences and spins </p><p>Viscosity</p><p>Preliminary</p><p>Statement of Sir Wm. Thomson's and Prof. Hicks's theories </p><p>General considerations concerning these theories </p><p>Description of the method here adopted </p><p>Acceleration in terms of the convergences their time-fluxes and the spins</p><p>Sir Wm. Thomson's theory </p><p>Prof. Hicks's theory</p><p>Consideration of all the terms except −∇ (σ2)/2 </p><p>Consideration of the term −∇ (σ2)/2 </p>