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 a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696. The brachistochrone curve is the same shape as the tautochrone curve; both are cycloids. However, the portion of the cycloid used for each of the two varies. More specifically, the brachistochrone can use up to a complete rotation of the cycloid (at the limit when A and B are at the same level), but always starts at a cusp. In contrast, the tautochrone problem can use only up to the first half rotation, and always ends at the horizontal. The problem can be solved using tools from the calculus of variations and optimal control. The curve is independent of both the mass of the test body and the local strength of gravity. Only a parameter is chosen so that the curve fits the starting point A and the ending point B. If the body is given an initial velocity at A, or if friction is taken into account, then the curve that minimizes time differs from the tautochrone curve. (Wikipedia).
AWESOME Brachistochrone problem
In this video, i set up and solve the brachistochrone problem, which involves determining the path of shortest travel in the presence of a downward gravitational field. This is done using the techniques of calculus of variations, and it will turn out that the brachistochrone can be represe
From playlist MECHANICS
AWESOME Brachistochrone problem II
In this video, i set up and solve the brachistochrone problem, which involves determining the path of shortest travel in the presence of a downward gravitational field. This is done using the techniques of calculus of variations, and it will turn out that the brachistochrone can be represe
From playlist MECHANICS
Brachistochrone Problem - Think you know which ramp is fastest?
Brachistochrone Problem - Take your best guess! Which path is the fastest? The answer lies in the math. The math reveals a very interesting shape in nature that pertains to any two points. Ready to see what the math reveals? BTW, A new field of mathematics known as the calculus of variati
From playlist Physics Demonstrations
Snell's law proof using springs
This is a supplement to the Brachistochrone video, proving Snell's law with a clever little argument by Mark Levi.
From playlist 3Blue1Brown | Math for fun and glory | Khan Academy
The Brachistochrone, with Steven Strogatz
Steven Strogatz and I talk about a famous historical math problem, a clever solution, and a modern twist. ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos
From playlist 3Blue1Brown | Math for fun and glory | Khan Academy
B24 Introduction to the Bernoulli Equation
The Bernoulli equation follows from a linear equation in standard form.
From playlist Differential Equations
Ex: Solve a Bernoulli Differential Equation Using an Integrating Factor
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations
Support Vsauce, your brain, Alzheimer's research, and other YouTube educators by joining THE CURIOSITY BOX: a seasonal delivery of viral science toys made by Vsauce! A portion of all proceeds goes to Alzheimer's research and our Inquisitive Fellowship, a program that gives money and resour
From playlist Science
Solve a Bernoulli Differential Equation Initial Value Problem
This video provides an example of how to solve an Bernoulli Differential Equations Initial Value Problem. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
Ex: Solve a Bernoulli Differential Equation Using Separation of Variables
This video explains how to solve a Bernoulli differential equation. http://mathispower4u.com
From playlist Bernoulli Differential Equations
The Transcontinental Burrito Hypertunnel (a Very Serious Science Video)
PBS Member Stations rely on viewers like you. To support your local station, go to: http://to.pbs.org/DonateOKAY ↓ More info and sources below ↓ We’re on PATREON! Join the community ►► https://www.patreon.com/itsokaytobesmart SUBSCRIBE so you don’t miss a video! ►► http://bit.ly/iotbs_sub
From playlist Be Smart - LATEST EPISODES!
Which path should you take? | Introduction to Calculus of Variations
Which path should you take? An introduction to Calculus of Variations. animations / visuals made using: manim: https://github.com/ManimCommunity/manim/ gslides: http://slides.google.com/ written math: my unprofessional tablet setup :3 social media stuff: webstie: https://ongzz.me instagr
From playlist Summer of Math Exposition Youtube Videos
How to Design the Perfect Shaped Wheel for Any Given Road
Last video, we looked at finding the ideal road for a square wheel to roll smoothly on, but what about other wheel shapes like polygons and ellipses? And what about the inverse problem: finding the ideal wheel to roll on any given road, such as a triangle wave? Previous episode: https://w
From playlist The Wonderful World of Weird Wheels
Solve a Bernoulli Differential Equation (Part 2)
This video provides an example of how to solve an Bernoulli Differential Equation. The solution is verified graphically. Library: http://mathispower4u.com
From playlist Bernoulli Differential Equations
B25 Example problem solving for a Bernoulli equation
See how to solve a Bernoulli equation.
From playlist Differential Equations