Learn Conical Coordinates with Mathworld

AI Thread Summary
Conical coordinates are primarily useful for describing geometries related to cones, as highlighted in discussions about their application in calculating geodesic distances on light cones. The transformation and Jacobian for conical coordinates are essential for understanding their mathematical properties. Several resources, including Mathworld and specific academic papers, provide insights and derivations related to these coordinates. A notable reference includes a paper by S. P. Drake and colleagues, which explores the causal association of electromagnetic signals using conical coordinates. Understanding these concepts can enhance the application of conical coordinates in various fields of physics and mathematics.
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Anyone here can teach me the conical coordinates?

I tried reading it in mathworld, but didn't understand it, anyone can give me the direct transformation, jacobian, some transforms and use of it?
 
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It seems to me that conical coordinates are only elegant when describing a cone..
 
My colleagues and I derived a set of conical coordinates to calculate the geodesic distance on the light cone (S. P. Drake, B. D. O. Anderson, and C. B. Yu, "Causal association of electromagnetic signals using the Cayley-Menger determinant," Applied Physics Letters 95 (3), 034106 (2009)).

These conical coordinates are also described here (http://www.physics.adelaide.edu.au/theory/staff/sdrake/conicalCoords.html" )
 
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