Activities

1. Use the spherical polar coordinates r and φ of the mass m to write the Lagrangian.
2. Check that φ is cyclic and that the corresponding constant of motion is L. Use the latter to write the one-dimensional problem describing the radial evolution. Check the expression of the effective potential energy.
3. How many circular orbits there exist for each value of L? Are they stable? Use the simulation to check your answers.
4. Is there any unbounded orbit? May the mass go to the cone apex?
5. Find a non-circular periodic orbit near E = 2.74.