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An approach to the pendulum problem, which is an alternative to the well-known traditional treatment of that problem, has been formulated. An advantage of the new approach is provided by a full symmetry in the position and momentum variables of the Hamiltonian expression for the energy of the system. A similar symmetry holds for the Hamilton equations describing the motion of a pendulum-like point mass. Calculations of the action function forthe two kinds of pendulum Hamiltonians - the traditional one and the new one - are presented.

Phase-space Symmetry and the Action Function of the Pendulum Problem