Turning points of the spherical pendulum and the golden ratio

Authors: Essén, H., Apazidis, N.
Document Type: Article
Pubstate: Published
Journal: European journal of physics
Volume: 30   427 - 432
Year: 2009


We study the turning point problem of the spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To put our result in perspective we briefly discuss its relevance in physics.