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Science · Advanced Physics
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-3. (10 points) Consider a particle of mass m constrained to move on the iside surface of a cone with angle 8. The axis of the cone is parallel to the axis z as shown in the figure. The surface of the cone is frictionless ad there is a unform gravitation feld莨=-gE (a) (3 points) Determine the Lagrangian of the particle b) (2 points) Determine the constants of motion (c) (2 points) Show that a particular solution consisting of a circular orbit of radius reto where r s the distance to the z axis. Discuss the conditions) under which such orbit happens of small oscillations of r around roe d) (3 points) Show that this orbit is stable w.rt. to small perturbations and find the frequency aL constant

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