TY - JOUR

T1 - Oscillations of a simple pendulum with extremely large amplitudes

AU - Butikov, Eugene I

PY - 2012

Y1 - 2012

N2 - Large oscillations of a simple rigid pendulum with amplitudes close to 180° 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 values for the period of large oscillations that coincide with high precision with the values given by the exact formula.

AB - Large oscillations of a simple rigid pendulum with amplitudes close to 180° 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 values for the period of large oscillations that coincide with high precision with the values given by the exact formula.

U2 - doi:10.1088/0143-0807/33/6/1555

DO - doi:10.1088/0143-0807/33/6/1555

M3 - статья

VL - 33

SP - 1555

EP - 1563

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 6

ER -