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j] represents spatial curvilinear coordinates in which j = 1, 2, 3 correspond to [phi], [OMEGA], and [theta].
Using tensor analysis, which is extremely useful especially for three-dimensional problems in any curvilinear coordinate system, a number of researchers, including Fung [4], Green and Zerna [5] have developed the general theory of elasticity.
This paper introduces the solution of the Poisson problem in a certain type of curvilinear coordinate domain and points out problems with it.
Sokolnikoff (4) developed a virtual work expression in general curvilinear coordinates.
After presenting the foundations in a form free from any coordinate system, the author follows with a chapter on the technique of writing Navier-Stokes equations and Euler's equations in general steady and nonsteady curvilinear coordinates, as well as the essential aspects of vorticity and stream functions.
A finite element method is developed from application of the principle of virtual work for the beam written in curvilinear coordinates in order to include the effects of finite deformation.