Some physical models with Minkowski spacetime structure and Lorentz group symmetry

Projecting the linear equation (X) over dot = AX, A is an element of so(n, 1), yields a primitive model. It is a prototype of several physical models, namely perfect elastoplasticity (on phase), spacetime of special relativit y, special relativistic mechanics and so on. all of which may endow a Minko wskian spacetime and the Lorentz group left acts on it. The mathematical st ructure of the perfect elastoplastic equations is then compared with those of the spacetime: of special relativity and of the special relativistic equ ations of motion of a massive charged particle, their similarities in group properties and subtle differences in phase spaces are discussed. It is rem arkable that the evolutions from elastic constitutive equations to elastopl astic constitutive equations and from the Newtonian equations to the specia l relativistic equations are very similar in several Facets, notably (a) fr om a linear theory to a non-linear theory, (b) the state space being enlarg ed from the usual Euclidean space to Minkowski spacetime. (c) from an n-spa ce to a cone of (n + 1)-space, (d) From a non-bounded state space to a boun ded state space, (e) from a non-causal relation of states to a causal relat ion of augmented states, (C) 2001 Elsevier Science Ltd. All rights reserved .