What is the brachistochrone curve used for?

In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) ‘shortest time’), or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides frictionlessly under the influence of …

Why is a brachistochrone curve the fastest?

The brachistochrone problem is one that revolves around finding a curve that joins two points A and B that are at different elevations, such that B is not directly below A, so that dropping a marble under the influence of a uniform gravitational field along this path will reach B in the quickest time possible.

What do mean by Brachistochrone 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 another in the least time. The term derives from the Greek (brachistos) “the shortest” and. (chronos) “time, delay.”

What is the equation of the Brachistochrone?

In other words, the brachistochrone curve is independent of the weight of the marble. Since we use the interpolation function int1 to approximate the curve , we can define a global variable T for the travel time using the formula given above: integrate(sqrt((1+(d(int1(x),x))^2)/max(0-int1(x),eps)),x,0,xB) .

Which curve is faster?

Brachistochrone curve
A Brachistochrone curve is the fastest path for a ball to roll between two points that are at different heights. A ball can roll along the curve faster than a straight line between the points. The curve will always be the quickest route regardless of how strong gravity is or how heavy the object is.

Who found Brachistochrone curve?

Johann Bernoulli
Finding the curve was a problem first posed by Galileo. In the late 17th century the Swiss mathematician Johann Bernoulli issued a challenge to solve this problem. He and his older brother Jakob, along with Gottfried Wilhelm Leibniz, Isaac Newton, and others, found the curve to be a cycloid.

Who discovered Brachistochrone?

brachistochrone, the planar curve on which a body subjected only to the force of gravity will slide (without friction) between two points in the least possible time. Finding the curve was a problem first posed by Galileo.

What is the isochronous curve?

The isochronous curve of Huygens is the curve such that a massive point travelling along it without friction has a periodic motion the period of which is independent from the initial position; the solution is an arch of a cycloid the cuspidal points of which are oriented towards the top; the fact that it is isochronous …

Is the brachistochrone a Tautochrone?

While the Brachistochrone is the path between two points that takes shortest to traverse given only constant gravitational force, the Tautochrone is the curve where, no matter at what height you start, any mass will reach the lowest point in equal time, again given constant gravity.