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The spherical curve obtained when moving along the surface of a sphere with constant speed, while maintaining a constant angular velocity with respect to a fixed diameter ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

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 x-axis, ...

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of ...

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 ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's equation is separable (either simply separable or R-separable). Bôcher (1894) ...

A curve on the surface of a sphere. Examples include the baseball cover, Seiffert's spherical spiral, spherical helix, and spherical spiral.

A closed geometric figure on the surface of a sphere which is formed by the arcs of great circles. The spherical polygon is a generalization of the spherical triangle. If ...

The volume of a spherical wedge is V=2/3r^3theta. The surface area of the corresponding spherical lune is S=2r^2theta.