Tautochrone curve

Four balls slide down a cycloid curve from different positions, but they arrive at the bottom at the same time. The blue arrows show the points' acceleration along the curve. On the top is the time-position diagram.

Five isochronous cycloidal pendula with different amplitudes.

A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity. The tautochrone curve is the same as the brachistochrone curve for any given starting point.

单词	Abel problem
释义	Abel problem 英语百科 Tautochrone curve A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point. The curve is a cycloid, and the time is equal to π times the square root of the radius over the acceleration of gravity. The tautochrone curve is the same as the brachistochrone curve for any given starting point.
随便看	flatter hammer flatter herself flatter himself flatteringly flattering flattering test flattering tool flattering unction flat terminal flatter myself flatter on flatter oneself flatter oneself that... flatter ourselves flatter product flatterrain flat terrain flatter ribbonlike fiber flatter ribbon like fiber flatter ribbonlike fibre flatter ribbon like fibre flatters out flatter themselves flatter to deceive flatter with

Abel problem

Tautochrone curve