Transformation of Coordinates (continued)

You can also transform in the other direction, i.e., from i j to e_r e_θ by dropping perpendiculars from e_r to i and e_θ to j as shown in the bottom right figure below.

Then use trigonometric relations to obtain the transformation from i and j to e_r and e_θ .

i = er cos θ - eθ sin θ

j = er sin θ + eθ cos θ

Note: As a check i . j = e_r . e_θ = 0

The same strategy of dropping perpendiculars and using trigonometric relations may be used for transformation from rectangular to normal and tangential descriptions.

i.e. i and j to e_n and e_t or vice-versus.

Likewise, the same strategy of dropping perpendiculars and using trigonometric relations may be

used to obtain a transformation from rectangular to an arbitrary coordinate system e_u and e_v

or vice-versus.

Click here for an example.

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Copyright © 2019 Richard C. Coddington
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