Consider the circular polar coordinate system {, } and its coordinate bases and orthonormal bases as shown in Fig. 24.3 and discussed in the associated

Consider the circular polar coordinate system {ω̅, ∅} and its coordinate bases and orthonormal bases as shown in Fig. 24.3 and discussed in the associated text. These coordinates are related to Cartesian coordinates {x, y} by the usual relations: x = ω̅ cos ∅, y = ω̅ sin ∅.

(a) Evaluate the components (L^x_ω̅, etc.) of the transformation matrix that links the two coordinate bases

Also evaluate the components (L^ω̅_x, etc.) of the inverse transformation matrix.

(b) Similarly, evaluate the components of the transformation matrix and its inverse linking the bases

(c) Consider the vector

What are its components in the other two bases?

Figure 24.3.

{x, ey} and {, }. e W