Talk:Tautochrone curve

Diagram request
I have added a simple diagram and I removed -reqdiagram- User:rocchini

question
Why arent the isochrone applications in astronomy mentioned?123.255.54.161 07:25, 21 October 2007 (UTC)

Visualization on a circle
The cycloid is the pattern produced by a rolling circle: thus a massless, frictionless circle, free to move along a track overhead, from the rim of which the mass is suspended, is equivalent to this track, and should have the same effect of producing a constant time. It would be interesting to see this treated mathematically and diagramatically in terms of the rotation of this circle. Wnt (talk) 18:38, 18 July 2008 (UTC)

Isochrone
I'm often seeing the word isochrone being used for maps whose contours/colours/edges show travel time using roads or public transport, e.g. http://airomaps.nuim.ie/flexviewer/?config=AIROAccessMap.xml -- is the phrase more general than just the curve described in this article? Ojw (talk) 22:10, 13 February 2012 (UTC) Yes, 'isochrone' on its own is just 'equal time', so any continuous set of points having some kind of 'equal time' property could equally be described as an isochrone or indeed an isochrone curve. This entry should describe a tautochrone (curve) as a specific kind of isochrone (curve) - presumably with the extra condition of arriving at the same point at the same time - and we could have a more generic entry, and point 'isochrone' disambiguation there.Cebderby (talk) 16:40, 11 October 2012 (UTC)

Virtual Gravity Solution
"The position of a mass measured along a tautochrone curve, s(t), must obey the following differential equation: [...]"

Oh, really? But this comes right out of nothing, from empty space. Well, I know that the harmonic oscillator does what is meant here, i. e., it provides a tautochrone. But is the opposite true? Why must a tautochrone be a harmonic oscillator?

And what is so "virtual" about the "Virtual gravity solution"? Methinks: nothing. It is simply the tangential component of the gravity vector. — Preceding unsigned comment added by 95.91.208.228 (talk) 17:24, 3 June 2022 (UTC)

Virtual Gravity solution
The final part, deriving the value of T, doesn't seem to compute. A factor of 4 appears. This may be because of changing from 2xtheta to phi. 86.188.71.235 (talk) 10:53, 16 August 2022 (UTC)

I don't think it's rolling along the x axis
It would have to be rolling along the line y=2r in contact and underneath it, not the line y=0 in contact and above. You want to end up with a bowl that will hold water, not a dome. 138.229.233.82 (talk) 08:22, 6 March 2023 (UTC)