Maths - Dual Complex Numbers - Forum Discusion - Robert

1. I'm looking at the page

https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/other/dualComplex/index.htm

Example - Combined Displacement and Rotation

where it says

Starting from the previous position:

(1 + 7ε + 7 iε)

and applying a rotation of 90 represented by:

(0 + i)

...

It would seem to me that this implies a counter clockwise rotation of 90 degrees. Yet the illustration of the automobile shows the the vehicle rotated CLOCKWISE at 90 degrees. This seems wrong to me. Below it says:

There seems to be a problem with the above, in that the rotation is in the opposite direction that I would have expected. Perhaps I have transposed the multipication table? Or perhaps the order of the multipication needs to be reversed? Can anyone help?

perhaps this is the answer to this question.

Robert Ramey

2. 2009-10-14 10:33:39 GMT

Robert,

Thank you very much for this. Looking back on it I am now reasonably sure that I reversed the order of multiplication, that is it should have the rotation on the left hand of the multiplication and the initial orientation on the right hand of the multiplication. When I do this the results are consistent and the rotation is anticlockwise as expected. I have updated the text and digram on the page to show this.

Cheers,

Martin