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Statement of a problem № 3446

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(a) A bead of mass m is constrained to move under gravity along a planar rigid wire that has a parabolic shape y = x^2/l , where x and y are, respectively, the horizontal and the vertical coordinates. Show that the Lagrangian for the system is L=m(x·)^2/2(1+4x^2/l^2)-mgx^2/l (b) Derive the Hamiltonian for a single particle of mass m moving in one dimension subject to a conservative force with a potential U (x ).

Solution:
(a)  A bead of mass m is constrained to move under gravity along a planar rigid

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