Deriving a Small Circle Equation in Spherical Coordinates: Any Pointers?

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SUMMARY

The discussion focuses on deriving the equation for small circles in spherical coordinates, specifically LONG(t) and LAT(t). The user explicitly requests methods for this derivation without switching to Cartesian coordinates. They also inquire about approximate equations and their accuracy. The conversation highlights the need for precise mathematical formulations in spherical geometry.

PREREQUISITES
  • Understanding of spherical coordinates
  • Familiarity with small circle equations
  • Basic knowledge of trigonometric functions
  • Experience with mathematical derivation techniques
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  • Research the derivation of small circle equations in spherical coordinates
  • Explore approximate equations for small circles and their accuracy
  • Study the applications of spherical coordinates in navigation and geodesy
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Mathematicians, physicists, and engineers working with spherical geometry, as well as students studying advanced coordinate systems.

whatta
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I need some good pointers to how could I derive arbitrary small circle equation in spherical coordinats (by hand or computer-aided), that is, LONG(t), LAT(t) or something like that.

Also, any approximate equations? How bad they are?

Please do not advice switching to cartesian, this is exactly what I would like to avoid.

Thank you for reading.

PS: if you happened to have ready equations, don't tease me, post'em.
 
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never mind, I have found the way around it. solution would still be good to know, but no longer necessary.
 

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