An element ds of arc length, in terms of dx and dy, is given by the theorem of Pythagoras: ds=((dx)2+(dy)2))1/2 or, since x and y are given by the parametric Equatio...An element ds of arc length, in terms of dx and dy, is given by the theorem of Pythagoras: ds=((dx)2+(dy)2))1/2 or, since x and y are given by the parametric Equations 19.1.1 and 19.1.2, by And of course we have just shown that the intrinsic coordinate ψ (i.e. the angle that the tangent to the cycloid makes with the horizontal) is equal to θ.
These equations are the parametric equations of a cycloid. (For more on the cycloid, see Chapter 19 of the Classical Mechanics notes in this series.) The motion is a circular motion in which the centr...These equations are the parametric equations of a cycloid. (For more on the cycloid, see Chapter 19 of the Classical Mechanics notes in this series.) The motion is a circular motion in which the centre of the circle drifts (hence the subscript D) in the x-direction at speed VD.
When the circle has rolled through an angle 2θ, the centre of the circle has moved to the right by a horizontal distance 2aθ, while the horizontal distance of the point P from the...When the circle has rolled through an angle 2θ, the centre of the circle has moved to the right by a horizontal distance 2aθ, while the horizontal distance of the point P from the centre of the circle is asin2θ and the vertical distance of the point P below the centre of the circle is acos2θ.
