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 Coordinates Introduction | Curvilinear Coordinate Sequence |
We usually do this activity after giving the students a brief introduction to cylindrical and spherical coordinates (e.g. Curvilinear Coordinates Introduction).
Curvilinear basis vectors make a nice example of a vector field: The basis vectors adapted to a single coordinate form a simple example of the geometrical notion of a vector field, i.e. a vector at every point in space. For example, the polar basis vectors \({\hat{r},\hat{\phi}}\) are shown in these figures
\(\hat{\theta}\) 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.
No wrap-up in needed beyond covering all the points listed in Student Conversations. The student handout solution can be provided to students. It contains figures that show the coordinate basis vectors at a single point.