New Vertically Planed Pendulum Motion

Author

Ismail, A. I.

Source

Mathematical Problems in Engineering

Issue

Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-6, 6 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2020-12-28

Country of Publication

Egypt

No. of Pages

6

Main Subjects

Civil Engineering

Abstract EN

This article is concerned about the planed rigid body pendulum motion suspended with a spring which is suspended to move on a vertical plane moving uniformly about a horizontal X-axis.

This model depends on a system containing three generalized coordinates.

The three nonlinear differential equations of motion of the second order are obtained to the elastic string length and the oscillation angles φ1 and φ2 which represent the freedom degrees for the pendulum motions.

It is assumed that the body moves in a rotating vertical plane uniformly with an arbitrary angular velocity ω.

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 approximated fourth-order Runge–Kutta method through programming packages.

These solutions are represented graphically to describe and discuss the behavior of the body at any instant for different values of the different physical parameters of the body.

The obtained results have been discussed and compared with some previously published works.

Some concluding remarks have been presented at the end of this work.

The value of this study comes from its wide applications in both civil and military life.

The main findings and objectives of the current study are obtaining periodic solutions for the problem and satisfying their accuracy and stabilities through the numerical procedure.

American Psychological Association (APA)

Ismail, A. I.. 2020. New Vertically Planed Pendulum Motion. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-6.
https://search.emarefa.net/detail/BIM-1201752

Modern Language Association (MLA)

Ismail, A. I.. New Vertically Planed Pendulum Motion. Mathematical Problems in Engineering No. 2020 (2020), pp.1-6.
https://search.emarefa.net/detail/BIM-1201752

American Medical Association (AMA)

Ismail, A. I.. New Vertically Planed Pendulum Motion. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-6.
https://search.emarefa.net/detail/BIM-1201752

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1201752