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?
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?
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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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