Deterministic chaos of a spherical pendulum under limited excitation

Shvets, A. Yu.

doi:10.1007/s11253-007-0039-7

Cited by 15 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The excitations u(t) and v(t) will excite the pendulum directly and are simply representative of synchronous forced vibration of the system, whereas the vertical motion w(t) will excite the pendulum through principal parametric resonance if the excitation is close to an integer multiple of the linear free damped natural frequency. The most significant throughput of mechanical energy in this direction will be when that integer mul-tiple is two [5,17,26], as required for principal parametric resonance. This multiplier of two is used for the complete numerical evaluation of this work, and therefore, this work is concerned with generic forcing.…”

Section: Model Of the Spherical Pendulum With Active Power Take-offmentioning

confidence: 99%

The dynamics of an omnidirectional pendulum harvester

Sommermann

Cartmell

2021

Nonlinear Dyn

View full text Add to dashboard Cite

The pendulum applied to the field of mechanical energy harvesting has been studied extensively in the past. However, systems examined to date have largely comprised simple pendulums limited to planar motion and to correspondingly limited degrees of excitational freedom. In order to remove these limitations and thus cover a broader range of use, this paper examines the dynamics of a spherical pendulum with translational support excitation in three directions that operate under generic forcing conditions. This system can be modelled by two generalised coordinates. The main aim of this work is to propose an optimisation procedure to select the ideal parameters of the pendulum for an experimental programme intended to lead to an optimised pre-prototype. In addition, an investigation of the power take-off and its effect on the dynamics of the pendulum is presented with the help of Bifurcation diagrams and Poincaré sections.

show abstract

Section: Model Of the Spherical Pendulum With Active Power Take-offmentioning

confidence: 99%

The dynamics of an omnidirectional pendulum harvester

Sommermann

Cartmell

2021

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…Krasnopolskaya and Shvets [7] considered the chaotic motion of deterministic parametric oscillations of a kinematically driven spherical pendulum. Later, Shvets [8] investigated the appearance, development, and vanishing of deterministic chaos in a ''spherical pendulum-electric motor of limited power'' dynamical system. He described discovered chaotic attractors.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

et al. 2020

View full text Add to dashboard Cite

This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.

show abstract