On the Motion of the Pendulum in an Alternating, Sawtooth Force Field

Abstract

The motion of the pendulum in a variable sawtooth force field is considered. For the “lower” equilibrium, the necessary stability conditions are investigated numerically, the results are presented in the form of an Ince–Strutt diagram. Using the Poincaré–Melnikov method separatrix splitting is studied analytically. Numerically, for some values of parameters, the nonlinear dynamics is studied using Poincaré maps, the regions of regular and chaotic behavior are revealed. The iterative method earlier proposed is used for the localization of periodic solutions, located inside the numerically identified “invariant tori”.