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Unified geometric and analytical treatment of magnetogasdynamic shocks. Part 1. General solutions and theorems

In this paper, the first of two parts on solutions to the non-relativistic de Hoffmann-Teller relations, a unified notation is developed and used to produce new analytical solutions for one-dimensional unsteady and two-dimensional crossed-fields representations. A simple numerical solution method for the non-aligned two-dimensional representation is also included. These solutions are explicit in the upstream parameters and a single strength parameter. Unification of reality, entropy and evolutionary conditions is also carried out. The resulting single criterion is used to derive algorithms by which the correct solution is obtained, in every case without previous computation and elimination of non-physical solutions. Classifications of the solutions are discussed in relation to previous schemes.