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Given the Lagrangian,being constant and t the time. a) Find the corresponding Hamiltonian. b) Is this Hamiltonian constant of motion? Explain. c) Show that the

Given the Lagrangian,being constant and t the time.

a) Find the corresponding Hamiltonian. b) Is this Hamiltonian constant of motion? Explain. c) Show that the Hamiltonian expressed in terms of the new variable, q = cos , and its momentum conjugate is not explicitly time dependent d) What physical system does this Hamiltonian represent? Explain

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