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Area Swept By The Radius Of Curvature Of A Function And Applications To Mechanics

Author

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  • Mehmet Pakdemirli

    (Department of Mechanical Engineering, Manisa Celal Bayar University 45140, Muradiye, Yunusemre, Manisa, Turkey)

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.

Suggested Citation

  • Mehmet Pakdemirli, 2024. "Area Swept By The Radius Of Curvature Of A Function And Applications To Mechanics," Acta Mechanica Malaysia (AMM), Zibeline International Publishing, vol. 7(1), pages 80-84, October.
    • Handle: RePEc:zib:zbnamm:v:7:y:2024:i:1:p:80-84
    DOI: 10.26480/amm.01.2024.80.84
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