Solve Exercise 3.1 by considering the transformation from XYZ to xyz to be the result of a sequence...

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Solve Exercise 3.1 by considering the transformation from XYZ to xyz to be the result of a sequence of body-fixed rotations.

Exercise 3.1

The XYZ coordinate system coincides with the edges of the box, the y axis coincides with the main diagonal for the box, and the x axis coincides with face ABCD. Use the orthonormal properties to determine the transformation that converts vector components relative to XYZ to components relative to xyz. Then use this transformation to determine the xyz coordinates of corner C.

David · Accepted Answer

AE= sqrt(.4*.4+.6*.6+.8*.8) = 1.077 
 
dc of angle AB/AE = .371, Ad/Ae= .557, CE/AE= .743 
 
Rotation matrix =   .832   -.555  0 
                            .371    .557   .743 
                           -.412   -.618    .670 
 
apply to the vector Rc= (.4,.6,0)   (0, .483,-.536)

Solve Exercise 3.1 by considering the transformation from XYZ to xyz to be the result of a sequence of body-fixed rotations. Exercise 3.1 The XYZ coordinate system coincides with the edges of the box,...

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