1.2.1 The Cycloid Problem
![The classic cycloid curve is generated by tracing the path of fixed point on the rim of a circle as it rolls on a flat surface. When the circle has radius one, the curve is parameterized by the path [math]\vec{c}\left(t\right)=\left(t-\sin t,1-\cos t\right),t\in\mathbb{R}[/math]](https://www.geogebra.org/resource/bbpbn8nm/NyDXOnd3SmPQFJ68/material-bbpbn8nm.png)
Which of the following describes ?
Define a vector as follows:
.
Describe this vector:
- What does this vector look like?
- Is it defined at all points along the path?
- When is it long?
- How long does it get?
- When does it vanish?
- In which direction does it point at each value of ?
Repeat the previous exercise for the vector .