Numerical and Analytical Investigation of the Dynamics of a Body Under the Action of a Periodic Piecewise Constant External Force

Abstract

AbstractThe paper investigates the dynamics of a body under the action of a piecewise constant periodic force with an arbitrary duty cycle and an oscillation limiter. Analytical relations for point mappings are presented for the first time using the Poincaré point mapping method. These relations allow one to study arbitrarily complex periodic motions both with a finite and infinite number of fixed points on the Poincaré surfaces. As a result, exact equations are presented in an analytical form that determine in the parameter space the existence and stability domains of periodic motions with an infinite number of fixed points on the Poincaré surfaces. The constructed with the help of a software product developed in the C++ language, bifurcation diagrams demonstrate, for some parameter values, the existence of chaotic regimes of body motion. Thus, the scenario for chaos origin is given. The comparison of numerical and analytical calculations is presented for different sets of parameters of the dynamical system.KeywordsNon-linear dynamicsPoint mapping methodChaotic regimes