First, a flat version of the problem: 1. Describe the trajectory of a weight sliding without friction along a spoke (infinitely long), if at the zero point of the spoke the weight has an initial velocity, and the spoke rotates in zero gravity with a constant angular velocity. Now the spherical version: 2. Describe the trajectory of a weight sliding along a rotating spoke in the shape of a circle. The spoke-ring rotates around an axis passing through the zero and opposite points of the ring.
The flat version has a solution in the form of a logarithmic spiral. I am also interested in solving the problem for a pendulum, that is, the spherical trajectory of the weight under gravity.
It turns out that the problem with a weight sliding along a rotating ring has a solution that coincides with the oscillations of a mathematical pendulum. Now we can try to find a solution to the problem in which a rotating ring with a weight slides along a rotating beam.
I have given the equation (3.19) of this physical model on page 10 (11)
Preprint Chaotic dynamics of an electron
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