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	ROUGHENING in photography的意思 roughening machine的意思 roughening, notching的意思 ROUGHENING of fibres的意思 roughening of ice on roads, traffic surfaces的意思 ROUGHENING of leather surfaces的意思 ROUGHENING of slippery road surfaces的意思 ROUGHENING of snow or ice for traffic purposes的意思 ROUGHENING of textile fabrics的意思 roughening on roads, traffic surfaces的意思 roughen的意思 roughening tool的意思 roughening transition的意思 roughening treads of pneumatic tyres的意思 roughening wheel的意思 roughen的意思 roughen up的意思 rough的意思 rougher的意思 rougher cell的意思 rougher cleaner flowsheet的意思 rougher floatation cell的意思 rougher flotation的意思 rougher mill的意思 rougher的意思

Abel problem

Tautochrone curve