AREA SWEPT BY THE RADIUS OF CURVATURE OF A FUNCTION AND APPLICATIONS TO MECHANICS

Mehmet Pakdemirli ()
Additional contact information
Mehmet Pakdemirli: Department of Mechanical Engineering, Manisa Celal Bayar University 45140, Muradiye, Yunusemre, Manisa, Turkey

Acta Mechanica Malaysia (AMM), 2024, vol. 7, issue 1, 80-84

Abstract: A new integral quantity is defined in this work. For a given function in a definite interval, a special integral is defined to calculate the area swept by the radius of curvature of the function. The basic definition, theorems and examples are given first. Using variational calculus, the function corresponding to the minimum area swept by its radius of curvature is given in the form of an ordinary differential equation. The differential equation is solved and plots of the functions are given. An approximate solution is also discussed within the context and contrasted with the numerical solution. Finally, two applications from mechanics, namely the deflection of beams and the dynamics of motion in a curved path are treated.

Keywords: Differential Equations; Variational Calculus; Perturbation Methods; Deflection of Beams; Kinematics (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://actamechanicamalaysia.com/archives/1amm2024/1amm2024-80-84.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:zib:zbnamm:v:7:y:2024:i:1:p:80-84

DOI: 10.26480/amm.01.2024.80.84

Access Statistics for this article

Acta Mechanica Malaysia (AMM) is currently edited by Dr. Alias B. Mohd

More articles in Acta Mechanica Malaysia (AMM) from Zibeline International Publishing
Bibliographic data for series maintained by Zibeline International Publishing ( this e-mail address is bad, please contact ).