The Brachistochrone With a Movable End-Point and the Nonsimultaneous Variations
2009 ◽
Vol 5
(1)
◽
Keyword(s):
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.
2008 ◽
Vol 55
(6)
◽
pp. 1279-1292
◽
1977 ◽
Vol 99
(2)
◽
pp. 85-90
◽
2006 ◽
Vol 321
(2)
◽
pp. 553-568
◽
2018 ◽
Vol 2018
◽
pp. 1-8
Necessary and sufficient conditions for oscillation of first-order functional differential equations
1990 ◽
Vol 148
(2)
◽
pp. 360-370
◽
2015 ◽
Vol 25
(10)
◽
pp. 1550135
◽