The dynamical behavior of a rigid body relative equilibrium position
type: Item
instance of: scholarly article
title: The dynamical behavior of a rigid body relative equilibrium position
zbMATH Open document ID: 1437.70005
DOI: 10.1155/2017/8070525
author: T. S. Amer
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: In this paper, we will focus on the dynamical behavior of a rigid body suspended on an elastic spring as a pendulum model with three degrees of freedom. It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity. The relative periodic motions of this model are considered. The governing equations of motion are obtained using Lagrange's equations and represent a nonlinear system of second-order differential equations that can be solved in terms of generalized coordinates. The numerical solutions are investigated using the fourth-order Runge-Kutta algorithms through Matlab packages. These solutions are represented graphically in order to describe and discuss the behavior of the body at any instant for different values of the physical parameters of the body. The obtained results have been discussed and compared with some previous published works. Some concluding remarks have been presented at the end of this work. The importance of this work is due to its numerous applications in life such as the vibrations that occur in buildings and structures.
Mathematics Subject Classification ID: 70E17
Mathematics Subject Classification ID: 37N05
zbMATH DE Number: 6962672
Wikidata QID: Q59142469
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/8070525
OpenAlex ID: W2593921991
cites work: Resonant motions of the three-dimensional elastic pendulum
cites work: Nonlinear normal modes in pendulum systems
cites work: Nonlinear control of a swinging pendulum
cites work: On global properties of passivity-based control of an inverted pendulum
cites work: Swinging up the spherical pendulum via stabilization of its first integrals.
cites work: The Simple Pendulum with Uniformly Changing String Length
cites work: A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method
cites work: On the Motion of the Pendulum on an Ellipse
cites work: On the relative periodic motions of a pendulum
cites work: Chaotic responses of a harmonically excited spring pendulum moving in circular path
cites work: Parametric control of oscillations and rotations of a compound pendulum (a swing)
cites work: Oscillations of a pendulum with a periodically varying length and a model of swing
cites work: Vibration reduction of a nonlinear spring pendulum under multi-parametric excitations via a longitudinal absorber
cites work: Vibration reduction of multi-parametric excited spring pendulum via a transversally tuned absorber
cites work: Asymptotic analysis of kinematically excited dynamical systems near resonances
description: scientific article; zbMATH DE number 6962672