Consider a mass m which is constrained to move on the frictionless surface of a vertical cone (opening angle alpha) in a uniform gravitational field gvertically down (Fig. 3).

Problem 3: Consider a mass m which is constrained to move on the frictionless surface of a vertical cone (opening angle a) in a uniform gravitational field g vertically down (Fig. 3). a) Write down the Hamiltonian and Hamilton's equations for this system using z and o as generalized coordinates. b) Consider a special case when the particle remains on a circu- lar orbit at fixed height z = zo. Show that if the orbit slightly devi- ates from the circular solution so that z = zo + 6 with e small, then e oscillates about zero with the angular frequency @ = 3g cosa. ZO