Alexandre Grothendieck's EGA V by Blass P., Blass J. PDF

By Blass P., Blass J.

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The expression in Eq. 73) which is the wrong result. 74) At this point, we do not have any criterion that indicates that the sign of Eq. 73) needs to be changed! Hence, attempting to find a from only the dyad a a is a dead end. Of course, one could always use the ˜Euler-Rodrigues ˜ ˜ to reconstruct the rotation tensor using Eq. 73). Then the axis formula direction could be reversed if the result does not equal the original rotation tensor. Again, this approach entails numerical round-off problems when trying to assess equality.

45) ˜ ˜ Thus, the cube of the axial tensor is just the negative of the axial tensor itself. Higher powers are computed similarly and alternate between being skewsymmetric axial tensors and (negative or positive) symmetric projectors. 47) ˜ ˜ ˜ ˜˜ ˜ ˜ ˜ Some proofs are most easily performed when the 3-direction is aligned with the rotation axis a , in which case ˜ c –s 0 0 –1 0 [ R ] = s c 0 and [ A ] = 1 0 0 ˜ ˜ 0 0 1 0 0 0 where c = cos α and s = sin α . 48) n T F A R D cca Rebe Brann May 9, 2002 3:49 pm Axis and angle of rotation on Argyris’s form of the Euler-Rodrigues formula.

73). Then the axis formula direction could be reversed if the result does not equal the original rotation tensor. Again, this approach entails numerical round-off problems when trying to assess equality. We now discuss a second approach. We have seen that solving the dyad a a for a is not a satisfactory method ˜ ˜ Below, ˜ we discuss an alternative for obtaining the principal rotation axis. method that instead finds the axial tensor A , from which the principal rota˜ tion axis may be found by applying Eq.

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Alexandre Grothendieck's EGA V by Blass P., Blass J.


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