On the motion of a triple pendulum system under the influence of excitation force and torque

In this article, a nonlinear dynamical system with three degrees of freedom (DOF) consisting of multiple pendulums (MP) is investigated. The motion of this system is restricted to be in a vertical plane, in which its pivot point moves in a circular path with constant angular velocity, under the action of an external harmonic force and a moment acting perpendicular to the direction of the last arm of MP and at the suspension point respectively. Multiple scales technique (MST) among other perturbation methods is used to obtain the approximate solutions of the equations of motion up to the third approximation because it is authorizing to execute a specific analysis of the system behaviour and to realize the solvability conditions given the resonance cases. The stability of the considered dynamical model utilizing the nonlinear stability analysis approach is examined. The solutions diagrams and resonance curves are drawn to illustrate the extent of the effect of various parameters on the solutions. The importance of this work is due to its uses in human or robotic walking analysis.