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#kinematics

mkwadee@diasp.eu
Khurram Wadee

Forgive the recent apparent obsession (I'd call it a fascination) with the #cycloid but I've just discovered something I'd not heard of before. It is also called a #TautochroneCurve or #Isochrone curve, which means that a particle starting from any location on the curve will get to the #MinimumPoint at precisely the same time as a particle starting at any other point.

Here's an #animation I wrote today in #Maxima which illustrates the property.

Tautochrone curve with animated particles

#Dynamics #Kinematics #Mathematics #AppliedMathematics #Mechanics #ClassicalMecanics #WxMaxima #FreeSoftware #MyWork #CCBYSA

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mkwadee@diasp.eu
Khurram Wadee

Imagine a circular wheel rolling, without skidding, on a flat, horizontal surface. The #locus of any given point on its #circumference is called a #cycloid. It is a #periodic #curve over a length equivalent to the #circle's circumference and has #cusps whenever the point is in contact with the surface (i.e. the two sides of the curve are tangentially vertical at that point).

Interestingly, it is also the curve that solves the #Brachistochrone problem, which means that starting at a cusp on the inverted curve (maximum height), a frictionless ball will roll under uniform gravity in minimum time from the start to any other point on the curve, even beating the straight line path.

#Mathematics #Geometry #Maths #AppliedMathematics #Mechanics #Kinematics #Dynamics #Physics #MyWork #CCBYSA #WxMaxima

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