Question

A classical Mechanics problem:

You have escaped from the university and are walking around Mt. Fuji in Japan, an active volcano. Suddenly, you feel Fuji-san begin to shake and you see extra smoke coming from its top. You want to know the shortest path from your current location on the mountain to your bus at the mountain’s base. That is, you want to find the geodesic for a cone. Recall that the geodesic on a sphere is a so-called “great circle,” the path an airplane takes when it travels long distances. Model Fuji-san as a cone so that you can use cylindrical coordinates with z = λ(1 − ρ), where ρ is the radial coordinate, z is the vertical coordinate and λ is merely a parameter that sets the steepness of the slope of Fuji-san. The azimuthal coordinate is denoted by φ. The required curve for the geodesic should be of the form φ = φ(ρ). Check your answer for the case λ → 0.

Answer 1

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