The Dynamical Behavior of a Rigid Body Relative Equilibrium Position
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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/8070525 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841524580474159104 |
|---|---|
| author | T. S. Amer |
| author_facet | T. S. Amer |
| author_sort | T. S. Amer |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eb0f8d1607ab4dc28bd28a86d085a78d |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-eb0f8d1607ab4dc28bd28a86d085a78d2025-02-03T05:52:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/80705258070525The Dynamical Behavior of a Rigid Body Relative Equilibrium PositionT. S. Amer0Department of Mathematics, Faculty of Science, Tanta University, Tanta 3127, EgyptIn 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.http://dx.doi.org/10.1155/2017/8070525 |
| spellingShingle | T. S. Amer The Dynamical Behavior of a Rigid Body Relative Equilibrium Position Advances in Mathematical Physics |
| title | The Dynamical Behavior of a Rigid Body Relative Equilibrium Position |
| title_full | The Dynamical Behavior of a Rigid Body Relative Equilibrium Position |
| title_fullStr | The Dynamical Behavior of a Rigid Body Relative Equilibrium Position |
| title_full_unstemmed | The Dynamical Behavior of a Rigid Body Relative Equilibrium Position |
| title_short | The Dynamical Behavior of a Rigid Body Relative Equilibrium Position |
| title_sort | dynamical behavior of a rigid body relative equilibrium position |
| url | http://dx.doi.org/10.1155/2017/8070525 |
| work_keys_str_mv | AT tsamer thedynamicalbehaviorofarigidbodyrelativeequilibriumposition AT tsamer dynamicalbehaviorofarigidbodyrelativeequilibriumposition |