Колебания маятника с предельно большими амплитудами

Abstract

Large oscillations of a simple rigid pendulum with amplitudes close to 180 degrees are treated on the basis of a physically justified approach in which the cycle of oscillation is divided into several stages. The major part of the almost closed circular path of the pendulum is approximated by the limiting motion, while the motion in the vicinity of the inverted position is described on the basis of the linearized equation. The accepted approach provides additional insight into the dynamics of nonlinear physical systems. The final simple analytical expression gives the values for the period of large oscillations that coincide with high precision with the values given by the exact formula based on the complete elliptic integral of the first kind.