Nonlinear dynamics of a gyro-rotor, and sensitive dependence on initial conditions of a heavy gyrorotor forced vibration/rotation motion

Abstract

The sensitive dependence of a heavy gyro-rotor around the two axes on the initial conditions of the forced vibration/rotation motion in the Earth gravitational field with linear and turbulent damping is studied using the nonlinear mechanics, chaos theory and dynamical systems. A generalization of the horseshoe arises in the Poincare map of the perturbed heavy gyro-rotor dynamics.