In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), or curve of fastest descent...

circle of radius R − 2r. Each hypocycloid (for any value of r) is a brachistochrone for the gravitational potential inside a homogeneous sphere of radius...

the acceleration of gravity. The tautochrone curve is related to the brachistochrone curve, which is also a cycloid. It was in the left hand try-pot of...

u'}}=C\,.} An example of an application of the Beltrami identity is the brachistochrone problem, which involves finding the curve y = y ( x ) {\displaystyle...

a lower point in the least possible time. He named the curve the "brachistochrone", (from brachystos, "shortest", and chronos, "time"): 31  Isaac Newton...

Bellman equation. While classical variational problems, such as the brachistochrone problem, can be solved using the Hamilton–Jacobi–Bellman equation,...

upward, is the curve of fastest descent under uniform gravity (the brachistochrone curve). It is also the form of a curve for which the period of an object...

but not without friction. Their most bitter dispute concerned the brachistochrone curve problem, or the equation for the path followed by a particle...

framework for studying transient dynamic waves in elastic solids. The brachistochrone problem can be formulated and expressed as a variational problem, emphasizing...

with Newton's minimal resistance problem in 1687, followed by the brachistochrone curve problem raised by Johann Bernoulli (1696). It immediately occupied...