Consider the curve traced by a point on the rim of a circle rolling along a straight line, a cycloid. If the cycloid were drawn in the xy-plane, then it could be described by the following position vector:
c(t)=(t-sin(t))i + (1-cos(t))j
Using MATLAB, how would i plot a cycloid for $0 \leq t \leq 6\pi$? How would i then find the velocity c'(t) of the moving point which traces the cycloid? I assume this could also be found using MATLAB but i have always been a bit rough with MATLAB expressions/inputs/etc. Lastly, is there a tool i could use to read off the graph to help find the exact length of a single arc?
Any help would be appreciated!! thanks! :)