Research Papers

The Brachistochrone With a Movable End-Point and the Nonsimultaneous Variations

[+] Author and Article Information
D. Radomirovic

 Faculty of Agriculture, Novi Sad, Serbia

Dj. Djukic, L. Cveticanin

 Faculty of Technical Sciences, Novi Sad, Serbia

J. Comput. Nonlinear Dynam 5(1), 011007 (Nov 18, 2009) (7 pages) doi:10.1115/1.4000316 History: Received October 07, 2008; Revised May 13, 2009; Published November 18, 2009; Online November 18, 2009

In this paper, the necessary and sufficient conditions for minima plane path with a movable end-point are developed. Using the calculus of variations the considered conditions are based on the zero first-order nonsimultaneous variation and on the positive second-order variation in the functional of integral type corresponding to mechanical systems. The applied procedure is the coordinate parametric method. The obtained solutions are tested on a brachistochrone with one end-point constrained to lie on a circle. The exact solution is compared with the approximate one obtained with Ritz’s method.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

The optimal bead path in vertical x–y coordinate plane



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In