the problem of finding the path between two points such that the transit time under specified conditions is minimized.
Questions tagged [brachistochrone-problem]
54 questions
25
votes
2 answers
Is there an intuitive reason the brachistochrone and the tautochrone are the same curve?
The brachistochrone problem asks what shape a hill should be so a ball slides down in the least time. The tautochrone problem asks what shape yields an oscillation frequency that is independent of amplitude. The answer to both problems is a…
Mark Eichenlaub
- 53,961
19
votes
3 answers
Another Solution To Brachistochrone Problem
Recalling the statement of the problem :
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the shortest time.
And as we can show with the method of…
Himanshu
- 12,211
18
votes
2 answers
Brachistochrone problem in general relativity
This question Brachistochrone Problem for Inhomogeneous Potential has the obvious extension. Namely the same question, when gravity is treated according to general relativity. To make it specific let's consider the case of Schwarzschild metric.…
MBN
- 3,875
10
votes
1 answer
Brachistochrone Problem for Inhomogeneous Potential
This recent question about holes dug through the Earth led me to wonder: if I wanted to dig out a tube from the north pole to the equator and build a water slide in it, which shape would be the fastest?
We're assuming a frictionless tube, of…
Mark Eichenlaub
- 53,961
9
votes
1 answer
What is the intuitive reason that the trajectory of a charged particle in a uniform crossed electro-magnetic field is a brachistochrone?
Cycloid is a type of trajectory which is traced by a point on the circumference of a planar circle rolling without slipping on a surface. It turns out that this is the solution to the Brachistochrone problem, that is the curve along which a material…
kbakshi314
- 2,430
8
votes
7 answers
Which block reaches the floor first?
There are two blocks, each starting at the top of an incline. The particular inclines are depicted in the image below.
The height through which the blocks fall is the same, the table lengths are the same, and the height of the tables is the same.…
Relativisticcucumber
- 1,987
8
votes
1 answer
Other kind of Brachistochrone problem
We know the Brachistochrone problem that to 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.
I wonder if we use a line segment mass…
Mathlover
- 541
7
votes
1 answer
What shape of track minimizes the time a ball takes between start and stop points of equal height?
I was at my son's high school "open house" and the physics teacher did a demo with two curtain rail tracks and two ball bearings. One track was straight and on a slight slope. The beginning and end points of the second track were the same but it was…
7
votes
1 answer
Brachistochrone problem for 3 points
I wonder how I can solve the Brachistochrone problem for 3 points?
The matter starts from point A that is the highest point and it must pass from B and must finish with point C. (No any friction in the system)
I wonder what the shortest time path…
Mathlover
- 541
5
votes
0 answers
Optimal tunnel shape for travelling inside the earth
Say you were to travel from Paris to Tokyo by digging a tunnel between both cities. If the tunnel is straight, one can easily compute that the time for travelling from one city to the other (independently from where both cities are actually) is a…
Mathusalem
- 1,023
5
votes
1 answer
Could two concatenated cycloids be an optimal solution to the Brachistochrone problem?
The following is a specific instance of the brachistochrone
problem, which I first encountered in grad school, and I
have occasionally used as hw problem in teaching CM.
A particle is started from rest at the origin and constrained to fall under…
Thomas
- 19,250
5
votes
1 answer
Brachistochrone problem with a limited slope angle and height
I'm trying to find the path of least time for a hollow sphere (a ping-pong ball) to roll from one point to another through an curve of interpolated points. The main problem here is that the ball isn't allowed to slide, only roll, which limits our…
Marcel
- 151
5
votes
2 answers
Path to obtain the shortest traveling time
Asume we have a particle sitting at the point A(0,0) in a gravitational field.
(g=9.81) It is going to move along some path to the point B(a,b) Where a>0 and b<0.
What is the curve the particle needs to be moving at to arrive at B in the
least time…
N3buchadnezzar
- 221
4
votes
1 answer
Brachistochrone problem with initial velocity
The Brachistochrone problem is usually presented with the having a ball dropped into the slide with initially zero velocity and at position $(x, y)=(0, 0)$.
I would like to know the more general solution to this problem. What happens when we start…
Swike
- 3,068
4
votes
1 answer
Is a brachistochrone a straight line in curved space?
Please bear with me, and don't get upset if i have lack in knowledge about spacetime.
Brachistochrone:
Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B…
user249036