Publisher's Synopsis
This book unifies the foundations, main concepts and equations of the kinematic theory of waves, ie the ray theory. It is believed to be the first in the literature to present the modern foundations of the non-linear theory of mechanics with singularities and contains a detailed discussion of the geometry of moving surfaces.;There is a step-by-step derivation of the kinematical and geometrical compatibility conditions for the first, second and higher order derivatives of a function which has jump discontinuities on the moving surface. The method of derivation is mathematically rigorous. The balance laws of dynamics and non-relativistic thermodynamics are formulated, and the corresponding balance equations obtained. No restriction is imposed on the class of admissible physical phenomena, so that the balance equations are applicable to any surface effect in a non-polar medium, particularly to the physics of interfaces, the theory of surface mass and energy concentration, to phase change effects and to wave propagation.;New results in wave analysis are formulated and proved, with special emphasis on the properties of shock waves and vortex sheets. Non-relativistic thermodynamics of a continuum with singularities is presented, along with the thermodynamics of interfaces.
