From these expressions, we see that computing exterior derivatives in a curvilinear coordinate
system is no different from computing in rectangular coordinates.
A distinguishing feature of the present paper is that for a thick shell of revolution with arbitrary curvature and variable thickness made of functionally graded materials, a set of field equations has been developed by tensor analysis in the curvilinear coordinate
This paper introduced the Sinc-Galerkin method for the Poisson problem in one type of curvilinear coordinate
Sokolnikoff (4) and McConnell (5) developed a generalized Hooke's law in curvilinear coordinates. The derivation is summarized below with all quantities evaluated at the current time t.
Then, the generalized Hooke's law for isotropic materials as provided in Sokolnikoff (4) in curvilinear coordinates becomes:
We have put into correspondence dual bases with direct and reciprocal bases of a curvilinear coordinates system, showing that physics defines geometry.
When dealing with laws of propagation of monochromatic plane waves, the so called "optical transformation theory" in stating an equivalence principle between electromagnetic parameters of a physical medium expressed in Cartesian coordinates and their analogues in vacuum obtained from a curvilinear coordinate transformation, puts in correspondence the Euclidean inhomogeneous and anisotropic physical space, with another homogeneous, isotropic and matter free space, but endowed with a locally flat metric.
Derivation of a Viscoelastic Constitutive Model in Curvilinear Coordinates
(2009), or a polar coordinate system as in Wang and Rose (2005), the governing equation is recast in terms of a local curvilinear system, formed by the curvilinear coordinate
s along the wall and the local wall radius of curvature [r.sub.cw].