Seiffert's spherical spiral is a
curve on a sphere made by moving on the sphere with constant speed and angular velocity with respect to a fixed diameter. If the selected diameter is the line from the north pole to the south pole, then the requirement of constant angular velocity means that the longitude of the moving point changes at a constant rate. The cylindrical coordinates of the varying point on this curve are given by the
Jacobian elliptic function
In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum, as well as in the design of electronic elliptic filters. While trigonometric functions are defin ...
s.
Formulation
Symbols
Representation via equations
The Seiffert's spherical spiral can be expressed in cylindrical coordinates as
or expressed as
Jacobi theta functions
.
See also
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Rhumb line
In navigation, a rhumb line, rhumb (), or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant azimuth ( bearing as measured relative to true north).
Navigation on a fixed course (i.e., s ...
References
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External links
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Spirals
Spherical curves
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