Find the expressions for the unit vectors in cylindrical coordinate system, p, φ,2. in terms of x, ý, 2. find the time-derivative of each. hints: unit vector p is defined in (x, y) plane. remember that α -φ is perpendicular to a the easiest way to find φ is to express rho through φ and add 90 degrees

Provided that the cylindrical coordinate system is given by the coordinates

The unit vectors are:

With their time derivatives being:

Explanation:

Let's start by writing the coordinate transformations:

,

,

.

For the unit vector we have:

For the unit vector we have:

By adding 90 degrees to , we have (see the 2nd attachment),

It is not hard to see that .

From this we can write the following useful expressions that we'll use later on to determine the time derivatives:

Now, knowing all of the above the time derivatives come in a straightforward way: