A Lagrangian and Hamiltonian formulation can be given for a damped harmonic oscillator with damping linear in the velocity. The canonical momentum is not equal to the kinetic momentum, and the Hamiltonian is not equal to the energy. On the other hand, a pendulum accreting mass has the same Lagrangian and equation of motion. However, in this case the canonical momentum is equal to the kinetic momentum, and the Hamiltonian is equal to the energy. No ambiguity arises if the physical situation is kept in mind.
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© 1986 American Association of Physics Teachers.
1986
American Association of Physics Teachers
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