Brachistochrone

brachistochrone

[brə′kis·tə‚krōn] (mechanics) The curve along which a smooth-sliding particle, under the influence of gravity alone, will fall from one point to another in the minimum time.

Brachistochrone

the curve of most rapid descent—that is, the one of all possible curves connecting two given points A and B of a potential force field that a mass point moving along the curve with an initial velocity equal to zero and acted upon only by the forces of the field will traverse from position A to position B in the shortest time. When the movement occurs in a homogeneous gravitational field, the brachistochrone is a cycloid with a horizontal base and a point of return that coincides with point A. The solution of the brachistochrone problem (Johann Bernoulli, 1696) served as the starting point for the development of the calculus of variations. The error of Galileo, who tried to prove that the brachistochrone is a circumferential arc, is instructive. (See G. Galilei, Izbrannye trudy, vol. 2, Moscow, 1964, pp. 298-301, note 465.)

单词	brachistochrone
释义	brachistochrone brachistochrone (brəˈkɪstəˌkrəʊn) n (Mathematics) maths the curve between two points through which a body moves under the force of gravity in a shorter time than for any other curve; the path of quickest descent[C18: from Greek brakhistos, superlative of brakhus short + chronos time] Brachistochrone brachistochrone [brə′kis·tə‚krōn] (mechanics) The curve along which a smooth-sliding particle, under the influence of gravity alone, will fall from one point to another in the minimum time. Brachistochrone the curve of most rapid descent—that is, the one of all possible curves connecting two given points A and B of a potential force field that a mass point moving along the curve with an initial velocity equal to zero and acted upon only by the forces of the field will traverse from position A to position B in the shortest time. When the movement occurs in a homogeneous gravitational field, the brachistochrone is a cycloid with a horizontal base and a point of return that coincides with point A. The solution of the brachistochrone problem (Johann Bernoulli, 1696) served as the starting point for the development of the calculus of variations. The error of Galileo, who tried to prove that the brachistochrone is a circumferential arc, is instructive. (See G. Galilei, Izbrannye trudy, vol. 2, Moscow, 1964, pp. 298-301, note 465.)
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