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 (Erdős 2000). This curve is given
in cylindrical coordinates by the parametric
equations
Erdős (2000) provides a derivation of the equations of this curve, as well as an analysis of its properties, including conditions for obtaining periodic orbits.
Bowman, F. Introduction to Elliptic Functions, with Applications. New York: Dover, p. 34, 1961.Erdős,
P. "Spiraling the Earth with C. G. J. Jacobi." Amer.
J. Phys.68, 888-895, 2000.Seiffert. "Über eine
neue geometrische Einführung in die Theorie der elliptischen Funktionen."
Wissensch. Beiträge Jahresber. Städtischen Realschule zu Charlottenburg,
Ostern. 1896.Whittaker, E. T. and Watson, G. N. A
Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University
Press, 1990.
is a positive constant and 
and 
are Jacobi elliptic
functions (Whittaker and Watson 1990, pp. 527-528).
