Chaos and order in librating quantum planar elastic pendulum

Mondal, Basudeb; Shah, Tirth; Chakraborty, Sagar

doi:10.1007/s11071-021-06267-9

Cited by 7 publications

(2 citation statements)

References 45 publications

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“…A simple pendulum has the most basic and comprehensive structure, which serves as the foundation for numerous complicated applications. Its significance in analysing the non-linear phenomena surrounding us is established in both engineering fields and fundamental areas such as physics and chemistry, and the lower dimensional compound system such as a swinging Atwood's machine [17], spring mass pendulum [18][19] and elastic pendulum [20][21][22] can demonstrate a wide variety of non-trivial phenomena including continuous processes and many types of resonance. A simple pendulum and another oscillating system, for example, a pendu-lum rotating with a different trajectory of its pivots, are components of different machine parts.…”

Section: Introductionmentioning

confidence: 99%

The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

Amir,

Ashraf,

Haider

2024

Acta Mechanica Et Automatica

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The dynamic analysis of complex mechanical systems often requires the application of advanced mathematical techniques. In this study, we present a variation iteration-based solution for a pendulum system coupled with a rolling wheel, forming a combined translational and rotational system. Furthermore, the Lagrange multiplier is calculated using the Elzaki transform. The system under investigation consists of a pendulum attached to a wheel that rolls without slipping on a horizontal surface. The coupled motion of the pendulum and the rolling wheel creates a complex system with both translational and rotational degrees of freedom. To solve the governing equations of motion, we employ the variation iteration method, a powerful numerical technique that combines the advantages of both variational principles and iteration schemes. The Lagrange multiplier plays a crucial role in incorporating the constraints of the system into the equations of motion. In this study, we determine the Lagrange multiplier using the Elzaki transform, which provides an effective means to calculate Lagrange multipliers for constrained mechanical systems. The proposed solution technique is applied to analyse the dynamics of a pendulum with a rolling wheel system. The effects of various system parameters, such as the pendulum length, wheel radius and initial conditions, are investigated to understand their influence on the system dynamics. The results demonstrate the effectiveness of the variation iteration method combined with the Elzaki transform in capturing the complex behaviour of a combined translational and rotational system. The proposed approach serves as a valuable tool for analysing and understanding the dynamics of similar mechanical systems encountered in various engineering applications.

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Section: Introductionmentioning

confidence: 99%

The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

Amir,

Ashraf,

Haider

2024

Acta Mechanica Et Automatica

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“…Its importance in understanding nonlinear occurrences about us is recognized in engineering disciplines as well as elementary areas such as physics and chemistry. Interestingly, a lower dimensional compound system, such as a double pendulum, swinging Atood’s machine 5 , elastic pendulum 6 – 8 , and spring-mass-pendulum 9 , 10 are sufficient to demonstrate an extensive range of non-trivial phenomena such as continuous processes and diverse categories of resonance. Several machine parts 5 – 10 are made up of a simple pendulum and another oscillating system such as a pendulum travelling in a plane or a pendulum revolving with different trajectories of their pivots.…”

Section: Introductionmentioning

confidence: 99%

Analytical solution for the motion of a pendulum with rolling wheel: stability analysis

Moatimid

Amer

2022

Sci Rep

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The current work focuses on the motion of a simple pendulum connected to a wheel and a lightweight spring. The fundamental equation of motion is transformed into a complicated nonlinear ordinary differential equation under restricted surroundings. To achieve the approximate regular solution, the combination of the Homotopy perturbation method (HPM) and Laplace transforms is adopted in combination with the nonlinear expanded frequency. In order to verify the achievable solution, the technique of Runge–Kutta of fourth-order (RK4) is employed. The existence of the obtained solutions over the time, as well as their related phase plane plots, are graphed to display the influence of the parameters on the motion behavior. Additionally, the linearized stability analysis is validated to understand the stability in the neighborhood of the fixed points. The phase portraits near the equilibrium points are sketched.

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Order and chaos around resonant motion in librating spring–mass–spherical pendulum

Das

Chakraborty

2021

Nonlinear Dyn

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Chaos and order in librating quantum planar elastic pendulum

Cited by 7 publications

References 45 publications

The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

The Variational Iteration Method for a Pendulum with a Combined Translational and Rotational System

Analytical solution for the motion of a pendulum with rolling wheel: stability analysis

Order and chaos around resonant motion in librating spring–mass–spherical pendulum

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