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Tagged with brachistochrone-problem variational-calculus
10
questions
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Find curve minimizing energy loss due to friction [closed]
I am looking for an ansatz of the following problem:
Given a mass $m$ moving in a constant gravitational field along curves $C$ connecting two fixed points I want to find the curve $C_0$ that ...
- 907
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1
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What is the definition of a Brachistochrone curve in a non-Euclidean space?
I have a problem where I have to study "the geometric properties of the Brachistochrone curve in non-Euclidean spaces". But I am confused about the definition of the Brachistochrone Problem/...
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Evaluating the integral in the brachistochrone problem numerically
When solving the brachistochrone problem (path of least time for a mass sliding on the path, with the path having no friction, from point A to point B), the solution curves are solved from the ...
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For virtual displacement in the Lagrangian, why is $\delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0$?
I am having trouble understanding why $$\delta \dot{x_i} = \delta \frac{dx_i}{dt} = \frac{d}{dt}\delta x_i \equiv 0.\tag{7.132}$$
you can see my explanation leading up to it below.
I would greatly ...
- 283
2
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2
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Brachistochrone to a vertical line [closed]
Just for fun, I am working through some problems in Mathematics of Classical and Quantum Physics by Byron and Fuller. Problem 2.13 reads:
Prove that a particle moving under gravity in a plane from a ...
- 147
9
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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 ...
- 2,402
3
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3
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Lagrangian Derivation of Brachistocrone? [closed]
I've been trying to derive the functional description of the brachistocrone. To do this, I used the Lagrangian to describe motion along a functional path. given a function $ f(x) $ where $0<y<a$ ...
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Optimal tunnel shape for travelling inside the earth [duplicate]
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 (...
- 993
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Why is a cycloid path the fastest way to roll a ball downward? [duplicate]
Possible Duplicate:
Path to obtain the shortest traveling time
I've been told that if one would want to make a ramp to get a ball from point A to a lower point B (at a certain horizontal distance ...
- 519
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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 ...
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