The bending of thin vertical rod and Bessel functions

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-48 Number-4
Year of Publication : 2017
Authors : Raghbir Dyal
  10.14445/22315373/IJMTT-V48P533

MLA

Raghbir Dyal "The bending of thin vertical rod and Bessel functions", International Journal of Mathematics Trends and Technology (IJMTT). V48(4):229-232 August 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
This paper is based on physical problem when anyone who has tried holding a long, thin, flexible rod in a vertical position. If the rod is short, and its tip is given a small sideways displacement and released , the rod will perform transverse oscillations until it reaches an equilibrium position in a bent shape because of supporting its own weight. The longer the road, the larger the amplitude of these oscillations and the greater the bending under its own weight when in equilibrium, until at some critical length the rod will bend until its tip just touches the ground, after which it will remain in that position.

Reference
1) Arfken, George B. and Hans J. Weber, Mathematical Methods for Physicists, 6th edition (Harcourt: San Diego, 2005). ISBN 0-12-059876-0.
2) Bayin, S. S. Mathematical Methods in Science and Engineering, Wiley, 2006, Chapter 6.
3) Bayin, S. S., Essentials of Mathematical Methods in Science and Engineering, Wiley, 2008, Chapter 11.
4) Bowman, Frank Introduction to Bessel Functions (Dover: New York, 1958). ISBN 0-486-60462-4.
5) B Spain, M. G. Smith, Functions of mathematical physics, Van Nostrand Reinhold Company, London, 1970. Chapter 9 deals with Bessel functions.
6) N. M. Temme, Special Functions. An Introduction to the Classical Functions of Mathematical Physics, John Wiley and Sons, Inc., New York, 1996. ISBN 0-471-11313-1. Chapter 9 deals with Bessel functions.

Keywords
until at some critical length the rod will bend until its tip just touches the ground, after which it will remain in that position.