Brachistochrone Problem

You should be very clear that under the influence of external fields, the obvious solution may be the most deceptive. A straight line is not so straight (or short ) any more See the legendary Brachistochrone Problem in Figure 5-8.1 had actually built this for a science project in my Physics days and, more recently, for my daughter s prize-winning science project. 

Bryce Canyon, a hillside of deciduous trees in autumn, the Overture of 1812, horses, a smiling little girl, Horsehead nebula, rings of Saturn, snow-capped mountain in a forest, palm trees on a Caribbean beach, newborn human infant, looks that pass between couples who have been happily married for 30 years, Ferrari Modena, Quebec City, the late Marian Anderson s voice, Newton s solution of the brachistochrone problem, a fresh pizza Martin Luther King Junior s I Have... 

Alipanah A, Razzaghi M, Dehghan M (2007) Nonclassical pseudospectral method for the solution of brachistochrone problem. Chaos, Solitons and Fractals 34 1622-1628... 

AUpanah A, Razzaghi M, Dehghein M (2007) Nonclassiceil pseudospectral method for the solution of brachistochrone problem. Chaos Solitons Fractals 34 1622-1628 Amsden AA, Harlow FH (1970) The SMAC method a numerictd technique for ctdculating incompressible fluid flows. Los Alamos Scientific Laboratory Report 4370 Andersson HI, Kristoffersen R (1989) Numerictd simulation of unsteady viscous flow. Arch Mech 41(2-3) 207-223... 

In Johann Bernoulli s problem, the brachistochrone, it is required to find the shape of a wire such that a bead slides from point 0, 0 to xi, yi in the shortest time T under the force of gravity. The energy equation mv2 = —mgy implies v = V—2gy, so that... 

To find the curve of quickest descent from one given point to another. Or, as Todhunter puts it, suppose an indefinitely thin smooth tube connects the two points, and a heavy particle to slide down this tube we require to know the form of the tube in order that the time of descent may be a minimum . This problem, called the brachistochrone (brachistos=shortest chronos=time), was first proposed by John Bernoulli in June, 1696, and the discussion which it invoked has given rise to the calculus of variations. Any book on mechanics will tell you that the velocity of a body which starts from rest is, page 376, Ex. (4),... 

After the problem of the brachistochrone had been solved, James Bernoulli, brother of John, proposed another variety of problem—the so-called isoperimetrical problem—of which the fol-... 

Calculus of variations seems to have started by solving brachistochrone (shortest time) problem. In 1696, Johann Bernoulli posed the following problem. Find the shape of the curve down which a bead sliding from rest and accelerated by gravity will slip (without friction) from one point to the other in the least time. It is said... 

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