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A system of coordinates obtained by inversion of the prolate spheroids and two-sheeted hyperboloids in prolate spheroidal coordinates. The inverse prolate spheroidal ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolas of parabolic cylindrical coordinates about the x-axis, ...

A system of curvilinear coordinates. There are several different conventions for the orientation and designation of these coordinates. Arfken (1970) defines coordinates ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

The adjective "affine" indicates everything that is related to the geometry of affine spaces. A coordinate system for the n-dimensional affine space R^n is determined by any ...

A system of curvilinear coordinates variously denoted (xi,eta,phi) (Arfken 1970) or (theta,eta,psi) (Moon and Spencer 1988). Using the notation of Arfken, the bispherical ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...

The Laplacian for a scalar function phi is a scalar differential operator defined by (1) where the h_i are the scale factors of the coordinate system (Weinberg 1972, p. 109; ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

When discussing a rotation, there are two possible conventions: rotation of the axes, and rotation of the object relative to fixed axes. In R^2, consider the matrix that ...