In this problem we find a good coordinate system to solve the problem of a mass constrained to the surface of a cone. Then, we calculate the Lagrangian of the system and use that with the Euler-Lagrange equation to solve for the equations of motion with each coordinate.
The constant polar angle, theta, is replaced with alpha in the problem.
In the video, it is mentioned that a coordinate transformation table might be helpful. Here is a link to one such website that runs down how to derive the formulas used for the Cartesian coordinate transformation. Do note, they use the angles Theta and Phi differently than I have used, but the process and results should follow.
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Music: [ Ссылка ]
