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brachistochrone    
最短时程; 最速降线; 捷线

最短时程; 最速降线; 捷线


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  • newtonian mechanics - Is there an intuitive reason the brachistochrone . . .
    The Brachistochrone condition is determined only by the force perpendicular to the curve, while the isochrone condition only cares that the force along the curve is linear in the arclength parametrization So it is easy to break the Brachistochrone condition while keeping the isochrone condition satisfied
  • variational principle - Another Solution To Brachistochrone Problem . . .
    In the brachistochrone problem, the motion of the body is given by the time evolution of the parameter: $$\phi(t)=\omega t, \ \ \omega =\sqrt{\frac{g}{r}}$$ Now, look at the angle, call $\theta$ , that the velocity vector makes with the vertical (Figure-B)
  • Why Does a Cycloid Curve Minimize Travel Time? - Physics Forums
    In the brachistochrone problem it is advantagious to have most of the acceleration early in the path You work up a lot of velocity early in the path, and then you benefit from that velocity for the rest of the duration Still, it's no good to cram all of the acceleration right at the start That is, it's no good to first drop straight down
  • Brachistochrone problem for 3 points - Physics Stack Exchange
    $^1$ Here I'm considering the idealized Brachistochrone problem where solution curves are allowed to be only piecewise smooth Instantaneous change of velocity (with no change in speed) is provided by an idealized (infinitely big) normal force, which does no work
  • Brachistochrone Problem w Initial Velocity - Physics Forums
    Some remarks on the brachistochrone problem (May, 2011) Marian Muresan Abstract This paper introduces some results on the brachistochrone problem with Coulomb friction and nonzero initial velocity The following boundary conditions are considered hereafter: fixed end points and fixed initial and final velocities
  • 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
  • Solution to Brachistochrone Problem - Physics Forums
    Can anybody post a full solution of the Brachistochrone problem provided by Newton (with full explanations) ? Or, any source about the same would be mu
  • energy conservation - 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 with initial velocity $\vec{v}_0 = (v_x, v_y)$?
  • How can you deepen your understanding of the brachistochrone problem?
    Homework Statement Hi I'm in second year of study in Math, Physic and Informatic and I require some help I began a work on the brachistochrone problem It's really interesting and I already found lot of things (the equation of the cycloid by the Bernoulli's method, I wrote some programs which
  • Is a brachistochrone a straight line in curved space?
    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 in the shortest time So from my understanding light moves in a 'straight' way (it moves in all ways but the outer paths cancel out?) And it always takes the fastest route





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