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Consider the Lagrangian for a bead on a rotating horizontal wire:
L = m/2 ( ̇q² + ω²q²).
(a) What is H? Is it constant?
(b) What if angular speed of rotation ω were not a constant? If ω = ω(t)
what is H? Would it be constant?
(c) In either case does H = E, the total energy.

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Consider the Lagrangian for a bead on a rotating horizontal wire: L = m/2 ( ̇q2 + ω2q2). (a) What is H? Is it constant? (b) What if angular speed of rotation ω were not a constant? If ω = ω(t) what is H? Would it be constant? (c) In either case does H = E, the total energy.