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Analytical Mechanics. Show step-by-step, please!

A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through a hole in a horizontal table. The string is pulled through the hole at a constant rate, so that the hanging length at time t is r = l – a t, where l and a are positive constants. Taking the angle the string makes with the vertical as a generalised coordinate, find the Hamiltonian for the system. Is the Hamiltonian the total energy? Is the Hamiltonian a constant of the motion? 7.1 -
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Transcribed Image Text:A particle of mass m oscillates in a vertical plane suspended by a massless string that goes through a hole in a horizontal table. The string is pulled through the hole at a constant rate, so that the hanging length at time t is r = l – a t, where l and a are positive constants. Taking the angle the string makes with the vertical as a generalised coordinate, find the Hamiltonian for the system. Is the Hamiltonian the total energy? Is the Hamiltonian a constant of the motion? 7.1 -
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