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

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”.

ON CHAOTIC BEHAVIOR OF A FIXED OFFSHORE STRUCTURE

In this paper we analyze the qualitative behavior of a fixed offshore oil platform under sea action perturbation (flows and tides), which is modeled by an inverted rigid pendulum with an elastic articulation at sea surface. We study their bifurcation properties provided by analytical framework and investigate their response to small oscillations, considered a more realistic case taking into consideration the platform features as flexibility and saturation. Our goal is to establish analytic conditions for chaotic oscillations occurrence in this model using the Poincaré–Mel'nikov's criterion for separatrix splitting in transverse orbits, considering external periodic force.