12.48. A particle of mass m moves in a central field attractive force of magnitude [k/r]e-a,...

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12.48. A particle of mass m moves in a central field attractive force of magnitude [k/r]e-a, where k and a are constants. Find the Lagrangian and Hamiltonian functions. Obtain Hamilton equations of motion. Is H constant? Is H the total energy? 12.49. A mass m is suspended by means of a string of length L that passes through a hole in a table. The string is pulled up at a constant rate k (cm/s); that is, dLldt constant, and the mass oscillates as a pendulum. Calculate the Lagrangian and Hamiltonian func- tions. Compare the Hamiltonian and the total energy, and discuss the conservation of energy for the system. Is it a constant of motion? Is it the total energy? Obtain Hamilton's equations of motion. -k. The suspension point remains %3D 12.48. A particle of mass m moves in a central field attractive force of magnitude [k/r]e-a, where k and a are constants. Find the Lagrangian and Hamiltonian functions. Obtain Hamilton equations of motion. Is H constant? Is H the total energy? 12.49. A mass m is suspended by means of a string of length L that passes through a hole in a table. The string is pulled up at a constant rate k (cm/s); that is, dLldt constant, and the mass oscillates as a pendulum. Calculate the Lagrangian and Hamiltonian func- tions. Compare the Hamiltonian and the total energy, and discuss the conservation of energy for the system. Is it a constant of motion? Is it the total energy? Obtain Hamilton's equations of motion. -k. The suspension point remains %3D