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Variations of the ray path and phase path: A Hamiltonian formulation
Author(s) -
Bennett J. A.
Publication year - 1973
Publication title -
radio science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.371
H-Index - 84
eISSN - 1944-799X
pISSN - 0048-6604
DOI - 10.1029/rs008i008p00737
Subject(s) - ordinary differential equation , path (computing) , hamiltonian (control theory) , mathematics , anisotropy , mathematical analysis , differential equation , physics , computer science , mathematical optimization , optics , programming language
Using a formulation based on Hamilton's ray equations, the variations of the path of a ray, and of the corresponding phase path, due to changes in the ray end points or the medium properties, are investigated. General expressions are obtained which represent the variations in terms of the solution of systems of ordinary differential equations. These may be integrated along the unvaried rays in order to evaluate the variations. The results, which may be applied to the analysis of a number of propagation problems, represent a simplification for anisotropic media and are also particularly well adapted to numerical applications.