Numerical and Experimental Study of Regular and Chaotic Motion of Triple Physical Pendulum

Abstract

Nonlinear dynamics of a real plane and periodically forced triple pendulum is investigated experimentally and numerically. Mathematical modeling includes details, taking into account some characteristic features (for example, real characteristics of joints built by the use of roller bearings) as well as some imperfections (asymmetry of the forcing) of the real system. Parameters of the model are obtained by a combination of the estimation from experimental data and direct measurements of the system's geometric and physical parameters. A few versions of the model of resistance in the joints are tested in the identification process. Good agreement between both numerical simulation results and experimental measurements have been obtained and presented. Some novel features of our real system chaotic dynamics have also been reported, and a novel approach of the rolling bearings friction modeling is proposed, among other.

Application of the generalized Prony spectrum for extraction of information hidden in chaotic trajectories of triple pendulum

“…In section 4 we collect as usual the basic results and discussion of possible applications of the GPS to other similar problems. Figure 1 exhibits a physical concept of a plane triple pendulum [3,4], with position being a function of three generalized coordinates: ψ 1 , ψ 2 and ψ 3 . Mass centers of the links are situated in the lines including the corresponding joints and their positions are described by the use of the parameters ( = 1 2 3).…”

“…The first link is externally forced by the torque 1 (τ). The motion of the pendulum set is governed by the following set of the dimensionless differential equations [3,4]:…”

Dynamics of a Pendulum of Variable Length and Similar Problems

“…System (31) has similar structure to system (26). That is why stability condition for its steady state solutions appears to be the same: cos(X 1 ) > 0.…”

“…It is often referred to simply as parametric pendulum, see e.g. [9,[22][23][24][25][26][27] and references therein. Stability and dynamics of EEP have been studied analytically and numerically in [28][29][30].…”

Nonlinear Dynamics Analysis of a Gear-Shaft-Bearing System with Breathing Crack and Tooth Wear Faults

“…Harsha [1] simulated some dynamic response of rotor supported by ball bearings, in his works non-linear dynamic responses were found to be associated with the ball passage frequency and severe vibrations occur when number of balls and waves of outer race are equal. Awrejcewicz [2][3][4] studied nonlinear characteristics of rotor bearing system using numerical method, instability regions of the rotor system were given for engineering applications. Dynamic behavior of gear-shaftbearing system is more complex because of time-varying mesh stiffness.…”