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# A horrid mistake in David Baraff's paper on Rigid Body Dynamics?

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I was reading Baraff''s paper on rigid body dynamics (found here: http://www-2.cs.cmu.edu/~baraff/sigcourse/notesd1.pdf) and I think I found an error ... and if it isn''t an error then it really confuses me. He says that the orientation of the rigid body is stored as 3x3 matrix, R. He then says that the position of any point in in the body''s local coordinate system can be transformed to the global coordinate system by multiplying the point with the matrix:
              [ Rxx  Ryx  Rzx ] [ x'' ]
[ x  y  z ] = [ Rxy  Ryy  Rzy ] [ y'' ]
[ Rxz  Ryz  Rzz ] [ z'' ]

He then (attempts) to drive home the fact that the orientation of the rigid body should be stored as a matrix by showing that the body''s local coordinate axes make up the elements of the matrix. This makes sense since it is just a basis. However, he shows it setting the [x'' y'' z''] matrix to [1 0 0], multiplying it by the rotation matrix, and showing what components in the matrix make up the x-axis. In his paper he somehow gets this:
position of the local point (1,0,0) in global space
[ x  y  z ] = [ Rxx  Rxy  Rxz ]

However, when I use my knowledge of simple matrix arithmetic I get this:
position of the local point (1,0,0) in global space
[ x  y  z ] = [ Rxx  Ryz  Rzx ]

I think his way is right since it is the columns of the matrix that form the basis, but the way he proved it seems wrong. So ... is his way right? And if so why does the way he proved it seem mathematically incorrect? Thanks ...

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it looks to me that you are wrong , you have to multiply the
components of the vector with the column of the matrix so
the first form of the first column of the resulting matrix is correct your version is a nonsense, try to look better at the matrix multyplications.

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Ohhh, ok, ok ... well, that''s why I posted ... I had been looking at the problem for about 30 mins and I knew I would never see it so I needed someone else to point it out ... well, thanks ...

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