Question

can anyone help me with this problem: Find the curvature of the highest point of an arc cycloid
x(t)=r(t-sin(t)) and y(t)=r-rcos(t)

Answer 1

http://en.wikipedia.org/wiki/Radius_of_curvature_(mathematics)

The curvature is given by

\[\kappa= \frac{\dot{x}\ddot{y}-\dot{y}\ddot{x}}{\sqrt{\dot{x}^2+\dot{y}^2}^3}\] With dot= differentiate wrt t.

If you've got curvature as a function of t, differentiate wrt to find stationary point, differentiate again again to find maximum.

Answer 2

*If you've got curvature as a function of t, differentiate wrt to find stationary point, differentiate again again to find out whether it is a maximum.

Answer 3

how can this be done? becuae im still not sure?