Basic Differential Models for Coordinate Generation,
MISSISSIPPI STATE UNIV MISSISSIPPI STATE DEPT OF AEROPHYSICS AND AEROSPACE ENGINEERING
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This paper examines in detail the analytical aspects of three distinct methods of coordinate generation based on partial differential equations, in either two or three dimensions. The first method is based on the Gauss equations of a surface under the constraint of the Beltramis second order equations. These equations have been structured in such a way that an automatic connection is established between the succeeding generated surfaces. The second method is a re-examination of those equations which are based on the inhomogeneous Laplace equations. This analysis reveals a new form for the terms which play a role in the concentration of coordinate lines and in the adaptive coordinate system generation. The third method pertains to a set of equations in the metric coefficients which is obtained by setting the Riemanns curvature tensor to zero.