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- Write the Lagrangian for a particle moving on a the surface of a cone of of half angle $\alpha$ assuming only gravitational forces. Assume that the vertex of the cone is downwards and that axis of the cone is vertical. Choose the $z-$ axis parallel to the axis of the cone.
- Write the Lagrangian and use conservation laws to obtain the solution of equations of motion in terms of quadratures.
- If the angular momentum of the particle is non zero, show that the motion is confined to the surface of the cone between two horizontal planes.
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