Students use their arms to depict (sequentially) the different cylindrical and spherical basis vectors at the location of their shoulder (seen in relation to a specified origin of coordinates: either a set of axes hung from the ceiling of the room or perhaps a piece of furniture or a particular corner of the room).
1. << Curvilinear Basis Vectors | Curvilinear Coordinate Sequence |
You will probably be doing this activity in-class, from directions given by the instructor. If you are doing it on your own, then choose a point in the room that you are in to be the origin. Imagine that your right shoulder is a point in space, relative to that origin. Point your right arm in succession in each of the directions of the basis vectors adapted the various coordinate systems:
- \(\left\{\hat{x},\hat{y},\hat{z}\right\}\) in rectangular coordinates.
- \(\left\{\hat{s},\hat{\phi},\hat{z}\right\}\) in cylindrical coordinates.
- \(\left\{\hat{r},\hat{\theta},\hat{\phi}\right\}\) in spherical coordinates.
We usually do this activity after giving the students a brief introduction to cylindrical and spherical coordinates (e.g. Curvilinear Coordinates Introduction).
\(\hat{\theta}\) should point generally downward: Make sure that the directions in which students point agree with the directions in the figures below.
In particular, \(\hat{\theta}\) should point generally downward.