Models of Particles and Moving Media

Book excerpt: Models of Particles and Moving Media deals with the use of mathematical models to study electrical interactions with moving particles and moving media. Topics covered range from space-time and the Galilean transformation to the Lorentz transformation of time and space and of Maxwell's equations. Forces and wave interaction with uniformly moving circuits and continua are also considered, along with non-uniform motion of charged particles in prescribed electric and magnetic fields. Comprised of seven chapters, this book begins with an overview of some of the ways in which motion can be described, with particular reference to the concept of space-time and the Galilean transformation. The discussion then turns to the Lorentz transformation of time and space, giving emphasis on the transformation of coordinates, time dilation and the Lorentz contraction, and conservation of mass and energy. After an analysis of the Lorentz transformation of Maxwell's equations, forces and wave interaction with uniformly moving circuits and continua are reviewed, along with non-uniform motion of charged particles in prescribed electric and magnetic fields. The book concludes by describing the use of the Lagrangian model and the Eulerian model to determine the motion of many interacting particles and the motion of charged and conducting fluids, respectively. This monograph is written primarily for students and researchers in the fields of mathematics and physics.